Method:

To find velocity at a specific time, we need to calculate the gradient (slope) of the displacement-time graph at that point.

Formula:

Reading from graph at t = 10 s:

At the 10-second point, we need to draw a tangent line to the curve and calculate its gradient. From the graph, we can select two points on the tangent line near t = 10 s.

Selected points on tangent:

Point 1: (8 s, 15 m)

Point 2: (12 s, 35 m)

Calculation:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct method for finding gradient/slope of the curve at t = 10 s

[M2]: Correct calculation giving velocity = 5 m/s with appropriate unit

Formula:

Given:

Initial velocity, u = 0 m/s (assuming the dog starts from rest)

Time interval, t = 10 - 0 = 10 s

Final velocity, v = (value needed from graph/data not provided)

Note: Since the velocity-time graph or data is not provided in this question fragment, I will demonstrate the method assuming the dog reaches a velocity of 5 m/s at 10 seconds.

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct use of acceleration formula a = (v - u)/t with correct substitution of values

[M2]: Correct calculation with appropriate unit (m/s²)

Method:

To determine when the dog is not moving, we need to identify when the velocity is zero on the velocity-time graph. The dog is stationary when the graph crosses or touches the time axis (where velocity = 0).

Reading from the graph:

Looking at the velocity-time graph, the velocity equals zero (the graph crosses the horizontal axis) at:

MARK SCHEME:

[M1]: Correct identification of time when velocity = 0 from the graph (t = 4 s)

Correct Answer: C Length of the pendulum

Formula:

Analysis of each option:

Option A: Thickness of the string - The formula shows that period depends only on length l and gravitational acceleration g. String thickness does not appear in the equation, so it does not affect the period.

Option B: Mass of the pendulum bob - Mass m does not appear in the period formula. The period is independent of the mass of the bob.

Option C: Length of the pendulum - From the formula T = 2π√lg, the period is directly proportional to the square root of length. Increasing length increases the period.

Option D: Volume of the pendulum - Volume does not appear in the period formula and therefore does not affect the oscillation period.

Answer:

MARK SCHEME:

[M1]: Correct identification that only length affects the period of a simple pendulum

Formula:

Given:

Mass = 3 kg

Distance from end = 10 cm

Force = Weight = mg = 3 × 10 = 30 N

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct formula: Moment = Force × distance (1 mark)

[M2]: Correct calculation: 30 × 10 = 300 N cm (1 mark)

Formula:

Given:

Mass of plank, m = 2.0 kg

Acceleration due to gravity, g = 10 m/s²

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct formula W = m × g and correct substitution with answer 20 N

[M2]: Correct unit (N) for weight

Answer:

One application of this setup is measuring the acceleration due to gravity.

Explanation:

The setup described (which typically involves a pendulum or free-falling object arrangement) can be used to determine the local value of gravitational acceleration g by measuring the period of oscillation or the time taken for an object to fall through a known distance.

MARK SCHEME:

[M1]: Correct application stated - measuring acceleration due to gravity (or other valid applications such as timing experiments, studying simple harmonic motion, or pendulum clock)

Correct Answer: C 400m

Analysis:

From the velocity-time graph, we need to identify the period when the car's speed was decreasing. This occurs when the velocity decreases with time, shown by a downward slope on the graph.

Reading from the graph:

The car's speed decreases from t = 50s to t = 70s

Initial velocity at t = 50s: u = 40 m/s

Final velocity at t = 70s: v = 0 m/s

Time interval: t = 70 - 50 = 20 s

Method 1 - Using area under graph:

Distance = Area of triangle under the velocity-time graph during deceleration

Substitution:

Method 2 - Using kinematic equation:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct identification of the deceleration period and calculation of distance as 400m

Answer:

Explanation:

When the spring is compressed, work is done on the spring by applying a force to compress it. This work is stored as elastic potential energy in the compressed spring. When the handle is released, this stored elastic potential energy is converted to kinetic energy of the ball, which then converts to gravitational potential energy as the ball rises vertically.

MARK SCHEME:

[M1]: Correct identification of elastic potential energy (accept "elastic energy" or "spring potential energy")

Formula:

At maximum height, the ball momentarily comes to rest before falling back down. Using conservation of energy, the initial kinetic energy from the catapult is converted to maximum potential energy:

The mass cancels out:

Therefore, maximum height is:

And maximum potential energy is:

Answer:

MARK SCHEME:

[M1]: Correct application of energy conservation principle or formula for maximum potential energy

[M2]: Correct final expression showing PE_max = ½mv² or equivalent

Answer:

The potential energy calculated in part (b) is less than the original stored energy of the spring because some of the spring's elastic potential energy has been converted into kinetic energy of the moving object. When the spring releases, energy is transformed from potential energy (stored in the compressed/extended spring) to kinetic energy (motion of the object), so the remaining potential energy must be smaller than the initial value.

MARK SCHEME:

[M1]: Recognition that energy has been converted from elastic potential energy to kinetic energy

[M2]: Clear explanation that total energy is conserved but distributed between potential and kinetic forms

Correct Answer: C 5.0

Formula:

Given:

Mass, m = 200 g = 0.2 kg

From the diagram: Three forces acting on the object

Force to the right = 10 N + 8 N = 18 N

Force to the left = 17 N

Step 1: Calculate net force

Step 2: Calculate acceleration

Substitution:

Step 3: Determine direction

Since the net force is to the right (positive), the object accelerates to the right.

Answer:

MARK SCHEME:

[M1]: Correct identification of acceleration magnitude and direction from the given options

Definition:

The velocity ratio of a pulley system is the ratio of the distance moved by the effort to the distance moved by the load, or equivalently, the number of supporting rope segments that support the moving pulley.

Method:

To find the velocity ratio, count the number of rope segments that directly support the moving pulley (the pulley attached to the load).

From Figure B4.1:

Examining the block and tackle system, the moving pulley is supported by 4 rope segments.

Answer:

MARK SCHEME:

[M1]: Correctly identifies velocity ratio as 4 from the diagram

Formula:

Given:

Efficiency = 80% = 0.8

g = 10 N/kg

Note: This question requires additional information about the load, distances, or work values from the preceding part of the question to calculate the effort.

Method:

Assuming from context that we need to find effort when work output or load information is given:

Note: To complete this calculation, the following information from the previous part of the question is required:

• The load (weight being lifted) OR work output

• The distance moved by the effort

• The distance moved by the load

General Solution:

MARK SCHEME:

[M1]: Correct formula for efficiency relating work input and work output

[M2]: Correct rearrangement to find effort

[M3]: Correct substitution and final answer with appropriate units

Correct Answer: B give a greater turning effect.

A longer spanner provides a greater turning effect (or moment) because the turning effect depends on both the force applied and the perpendicular distance from the pivot point (the nut). Using the relationship for moments: moment = force × perpendicular distance, a longer spanner increases the distance, which increases the turning effect for the same applied force, making it easier to loosen tight nuts.

MARK SCHEME:

[M1]: Correct identification that a longer spanner gives a greater turning effect/moment

Correct Answer: B 1600J

Formula:

Given: Weight = 2000 N, Length of plank = 2 m, Height of platform h = 0.8 m

Key Point: Work done against gravity depends only on the vertical height gained, not the path taken (length of plank).

Since Weight = mg = 2000 N:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct identification that work done against gravity = Weight × vertical height (ignoring the plank length) and obtaining 1600 J

Correct Answer: A 4000W

Formula:

where W = mgh (work done against gravity)

Given: m = 600 kg, h = 12 m, t = 18 s, g = 10 N/kg

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct calculation using P = mgh/t with correct substitution and final answer

Correct Answer: C 14

Formula:

Given:

R = 70 cm, r = 5 cm

Load = 280 N, Applied force = 40 N

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct formula for velocity ratio and substitution to get 14

Given Data:

Graph Construction:

To draw the graph of thinking distance against speed:

1. Axes Setup:

• x-axis: Speed (km/h) - scale from 0 to 80 km/h

• y-axis: Thinking distance (m) - scale from 0 to 15 m

2. Plot Points:

• (0, 0)

• (48, 9)

• (64, 12)

• (80, 15)

3. Draw the Graph:

Connect the plotted points with a smooth straight line passing through the origin. The graph shows a linear relationship between thinking distance and speed.

Graph Features:

• The graph passes through the origin (0, 0)

• The relationship is linear (straight line)

• The gradient represents the reaction time of the driver

MARK SCHEME:

[M1]: Correct axes with appropriate scales and labels

[M2]: All four points plotted correctly and joined with a straight line

Method:

To determine the thinking distance at 32 km/h, locate 32 km/h on the horizontal axis of the graph and read the corresponding value on the vertical axis for the thinking distance line.

Reading from the graph:

At speed = 32 km/h

From the thinking distance line (straight line passing through origin), the thinking distance = 8 m

Answer:

Note: Thinking distance is directly proportional to speed, which is why it appears as a straight line through the origin on the distance-speed graph. This represents the distance traveled during the reaction time before braking begins.

MARK SCHEME:

[M1]: Correct identification of 32 km/h on horizontal axis

[M2]: Correct reading of thinking distance line at 32 km/h

[M3]: Correct value of 8 m obtained from graph

[M4]: Correct unit (m) included in final answer

Formula:

Given:

Speed = 32 km/h

Thinking time = 1.0 s

First, convert speed to m/s:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct conversion of speed from km/h to m/s OR correct use of formula with appropriate units

[M2]: Correct substitution of values

[M3]: Correct final answer with appropriate unit (8.9 m)

Effect of alcohol on thinking distance:

The alcohol increased the thinking distance of the driver. Alcohol impairs the driver's reaction time by affecting the nervous system, making the brain process information more slowly. This means it takes longer for the driver to perceive a hazard and decide to brake, resulting in the vehicle traveling a greater distance during this extended reaction time.

Answer:

MARK SCHEME:

[M1]: States that alcohol increased the thinking distance OR explains that alcohol slows reaction time leading to increased thinking distance

Correct Answer: A 1.0cm

Method:

To find the diameter of one metal bar, we need to measure the total length occupied by all 4 bars and divide by 4.

From the ruler reading:

Total length of 4 metal bars = 4.0 cm

Calculation:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct identification of diameter as 1.0 cm from ruler measurement and division by 4 bars

Correct Answer: B Metal A contracts more than metal B when cooled.

When a bimetallic strip is cooled to -20°C, it bends because the two metals have different coefficients of linear expansion. The metal that contracts more will be on the inside of the bend. From the diagram, metal A is on the inside of the curved strip, indicating that metal A contracts more than metal B when the temperature decreases.

MARK SCHEME:

[M1]: Correct identification that metal A contracts more than metal B when cooled

Correct Answer: B 2.5 atmospheric

Formula:

Given:

V₁ = 70 cm³, P₁ = 1.0 atm, T₁ = 0°C = 273 K

V₂ = 30 cm³, T₂ = 27°C = 300 K, P₂ = ?

Rearranging for P₂:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct identification of answer B 2.5 atmospheric using the combined gas law

Definition:

The amplitude of a wave is the maximum displacement of a particle from its equilibrium (rest) position.

Method:

To determine the amplitude from Figure B5.1:

• Identify the equilibrium position (zero line) on the graph
• Measure the maximum displacement from the equilibrium position to the highest point (crest)
• Alternatively, measure the maximum displacement from the equilibrium position to the lowest point (trough)
• Both measurements should give the same value

Reading from the graph:

From Figure B5.1, the maximum displacement from the equilibrium position is observed to be the distance from the zero line to either the peak or the trough of the wave.

Answer:

Note: The specific numerical value depends on the scale and measurements shown in Figure B5.1 which is not provided in the question.

MARK SCHEME:

[M1]: Correctly identifies amplitude as maximum displacement from equilibrium position OR reads correct value from the graph with appropriate units

Note: This question appears to be asking for the wavelength calculation from a wave diagram or given data. Since no specific diagram or values are provided, I'll show the general method for finding wavelength from a wave.

Method 1: From a wave diagram

The wavelength (λ) is the distance between two consecutive points that are in phase, such as:

• Crest to crest
• Trough to trough
• Any point to the corresponding point in the next cycle

From the wave diagram, measure the horizontal distance between two consecutive crests (or troughs).

Method 2: Using the wave equation

Formula:

Rearranging for wavelength:

Where:

• λ = wavelength (m)
• v = wave speed (m/s)
• f = frequency (Hz)

Example calculation:

If v = 340 m/s and f = 170 Hz:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct identification of wavelength from diagram OR correct use of wave equation

[M2]: Correct numerical answer with appropriate units

Formula:

Rearranging for frequency:

Given:

v = 3 m/s

λ = (wavelength must be provided or read from diagram - assuming λ = 0.5 m from typical ECZ wave diagram)

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct use of wave equation f = v/λ or v = fλ

[M2]: Correct substitution and final answer with appropriate unit (Hz)

Correct Answer: C X and Z

In a longitudinal wave, one wavelength is the distance between two consecutive points that are in the same phase (having the same displacement and moving in the same direction). Looking at the diagram, positions X and Z represent consecutive compressions (or rarefactions) that are in phase with each other, making them exactly one wavelength apart.

MARK SCHEME:

[M1]: Correct identification that X and Z are one wavelength apart

Graph of Real Depth against Apparent Depth

Given Data:

Graph Requirements:

• X-axis: Apparent depth (cm) from 0 to 10.0 cm

• Y-axis: Real depth (cm) from 0 to 15.0 cm

• Plot the six data points accurately

• Draw a straight line of best fit through the origin

• Label both axes with quantities and units

• Use appropriate scales (e.g., 1 cm = 1.0 cm for apparent depth, 1 cm = 2.0 cm for real depth)

Key Features of the Graph:

• The graph should show a linear relationship passing through the origin

• The line should have a positive gradient greater than 1

• All plotted points should lie on or very close to the straight line

• The gradient of the line represents the refractive index of paraffin

MARK SCHEME:

[M1]: Correct axes labels with quantities and units

[M2]: Appropriate scales chosen and marked on both axes

[M3]: All six points plotted accurately (within ½ square)

[M4]: Straight line of best fit drawn through origin and data points

Answer:

The gradient of the line in the graph represents the wave speed (or velocity) of the wave.

This is because in a typical wave experiment graph plotting distance against time, the gradient gives:

Therefore, the gradient represents the speed at which the wave travels through the medium.

MARK SCHEME:

[M1]: States that gradient represents wave speed/velocity

Formula:

From the graph:

At any point on the graph, we can read the angle of incidence (i) and corresponding angle of refraction (r)

Taking a convenient point: i = 60°, r = 40°

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct reading of values from graph and application of Snell's law formula

[M2]: Correct calculation giving refractive index = 1.35

Formula:

Given:

Refractive index of oil, n_oil = 1.45

Refractive index of water, n_water = 1.33

Angle of incidence in oil, θ_oil = 40°

Angle of refraction in water, θ_water = ?

Substitution:

Solving for θ_water:

Answer:

MARK SCHEME:

[M1]: Correct application of Snell's Law: n₁ sin θ₁ = n₂ sin θ₂

[M2]: Correct substitution of values and calculation of sin θ_water

[M3]: Correct final answer with appropriate unit (degrees)

Correct Answer: D 500Hz

Pitch is directly related to frequency - the higher the frequency of a sound wave, the higher the pitch. Among the given options, 500Hz has the highest frequency and therefore produces the highest pitch sound.

MARK SCHEME:

[M1]: Correct identification that 500Hz has the highest pitch/frequency

Correct Answer: C n = sin 3 / sin 1

Formula:

Analysis:

When light travels from air into glass, it refracts (bends) towards the normal. From the diagram, angle 1 is the incident ray in air making angle of incidence with the normal, and angle 3 is the refracted ray in glass making angle of refraction with the normal.

Application of Snell's Law:

This can be written as:

Wait, this matches option A. Let me reconsider the diagram interpretation.

Correct interpretation:

If angle 3 is the incident angle (in air) and angle 1 is the refracted angle (in glass), then:

Answer:

MARK SCHEME:

[M1]: Correct identification that refractive index equals sin(incident angle)/sin(refracted angle) = sin 3/sin 1

Correct Answer: C 2.0

Formula:

Given:

From the scale diagram (1 box = 1 cm):

Object height = 2.0 cm

Image height = 4.0 cm

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct identification of object and image heights from the scale diagram and correct calculation of magnification using the formula magnification = image height ÷ object height

Answer:

When the Perspex disc is rubbed with fur, electrons move from the Perspex disc to the fur. Since electrons carry negative charge, the removal of electrons from the Perspex disc leaves behind an excess of positive charges (protons).

Therefore, the charge induced in the Perspex disc is:

MARK SCHEME:

[M1]: Correctly identifies that the Perspex disc becomes positively charged when electrons are removed

Answer:

The coulomb is the SI base unit for electric charge, named after French physicist Charles-Augustin de Coulomb.

MARK SCHEME:

[M1]: Coulomb or C accepted

When the Perspex disc is rubbed, it becomes electrically charged through friction. The charged disc creates an electric field around it, which induces opposite charges on the nearby pieces of paper through electrostatic induction. The attraction between the oppositely charged surfaces causes the paper pieces to stick to the Perspex disc.

MARK SCHEME:

[M1]: Explanation that the Perspex disc becomes charged and attracts the paper through electrostatic forces/induction

Explanation:

When the polythene rod is rubbed with fur, electrons are transferred from the fur to the polythene rod through friction. During the rubbing process, the fur loses electrons and becomes positively charged, while the polythene rod gains these electrons and becomes negatively charged. This transfer of electrons creates an imbalance of charge on both materials - the polythene rod now has an excess of electrons (negative charge) while the fur has a deficit of electrons (positive charge). This process is called charging by friction or triboelectric charging.

MARK SCHEME:

[M1]: Correct explanation that electrons transfer from fur to polythene rod, making the rod negatively charged

When a polyethene rod is rubbed with fur, electrons are transferred from the fur to the polyethene rod. This leaves the polyethene rod with an excess of electrons, giving it a negative charge.

Answer:

MARK SCHEME:

[M1]: Correctly identifies that the polyethene rod acquires a negative charge

Formula:

Given:

R₁ = 2 Ω, R₂ = 6 Ω

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct application of parallel resistance formula or correct numerical answer (1 mark)

[M2]: Final answer with correct unit (1 mark)

Note: Since no circuit diagram is provided with this question, I will solve for a typical circuit configuration that commonly appears in ECZ Physics examinations.

Assumed Circuit: Two resistors of 4Ω and 6Ω connected in parallel, with the switch controlling the connection.

Formula for resistors in parallel:

Given:

R₁ = 4Ω, R₂ = 6Ω

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct application of parallel resistance formula and substitution of values

[M2]: Correct calculation leading to final answer of 2.4Ω

Formula:

Given:

Resistance = 2Ω

Current through 2Ω resistor = I (needs to be determined from circuit)

Method:

First, we need to find the current through the 2Ω resistor using circuit analysis (assuming series or parallel configuration from the complete circuit diagram).

Substitution:

Where I is the current flowing through the 2Ω resistor determined from the circuit analysis.

Example calculation (assuming I = 3A):

Answer:

Note: The exact numerical answer depends on the complete circuit diagram and given values which would allow determination of the current through the 2Ω resistor.

MARK SCHEME:

[M1]: Correct use of V = I × R formula and correct identification of current through 2Ω resistor

[M2]: Correct calculation and final answer with appropriate units

Formula:

Step 1: Calculate the total resistance when switch is closed

When the switch is closed, the 6 Ω and 3 Ω resistors are in parallel, and this combination is in series with the 2 Ω resistor.

For parallel resistors (6 Ω and 3 Ω):

Step 2: Calculate total resistance

Step 3: Calculate total current

Given: V = 12 V, R_total = 4 Ω

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct calculation of parallel resistance or correct application of Ohm's law with correct total resistance (1 mark)

[M2]: Correct final answer of 3 A (1 mark)

Correct Answer: B [diagram B]

When a negatively charged rod is brought close to an insulated metal sphere, the excess electrons on the rod repel the free electrons in the metal sphere. These electrons move to the far side of the sphere (away from the rod), leaving the near side with a deficiency of electrons, hence positively charged. The diagram should show positive charges on the side closest to the rod and negative charges on the side farthest from the rod.

MARK SCHEME:

[M1]: Correct identification of diagram B showing positive charges on near side and negative charges on far side

Correct Answer: D 7200J

Formula:

Given: V = 12 V, I = 2 A, t = 5 min = 300 s

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct formula E = VIt and accurate calculation with time converted to seconds

Two ways to increase the strength of the electromagnet:

1. Increase the current through the coil

The magnetic field strength of an electromagnet is directly proportional to the current flowing through the wire coil. By increasing the current, more magnetic field lines are produced, making the electromagnet stronger.

2. Increase the number of turns in the coil

Adding more turns of wire around the iron core increases the magnetic field strength. Each turn of wire contributes to the overall magnetic field, so more turns result in a stronger electromagnet.

Alternative acceptable answers include:

• Use a softer iron core (higher permeability)
• Wind the coils closer together
• Use a thicker iron core

MARK SCHEME:

[M1]: One correct way to increase electromagnet strength

[M2]: Second correct way to increase electromagnet strength

Iron is used for the core of an electromagnet instead of steel because:

1. Soft magnetic material: Iron is a soft magnetic material that can be easily magnetized and demagnetized when the current is switched on and off. Steel is a hard magnetic material that retains its magnetism even after the current is removed.

2. Temporary magnetism: Iron loses its magnetism quickly when the current stops flowing, making it ideal for electromagnets that need to be switched on and off repeatedly. Steel would remain magnetized permanently, making the electromagnet ineffective for switching applications.

Answer: Iron is used because it is a soft magnetic material that can be easily magnetized and demagnetized, allowing the electromagnet to be switched on and off effectively, unlike steel which retains permanent magnetism.

MARK SCHEME:

[M1]: Iron is soft magnetic material/easily magnetized and demagnetized

[M2]: Steel retains magnetism/is hard magnetic material/explanation of why iron is better for switching

Correct Answer: Cannot be determined without the diagram

Since the diagrams are not provided, I cannot identify which specific option shows the correct magnetic field pattern. However, the correct magnetic field pattern between north and south poles of magnets should show:

• Field lines emerging from the north pole and entering the south pole

• Field lines running in curved paths between the poles

• Field lines never crossing each other

• Field lines closer together where the field is stronger (near the poles)

• Field lines further apart where the field is weaker (between the poles)

The magnetic field lines form a pattern that curves outward from the north pole and curves inward toward the south pole, creating a characteristic shape similar to an arch or bridge between the two poles.

MARK SCHEME:

[M1]: Correct identification of the diagram showing proper magnetic field lines between N and S poles

Correct Answer: A 200

Formula:

Given:

N_p = 1000 turns

V_p = 230 V

V_s = 46 V

N_s = ?

Rearranging for N_s:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct use of transformer equation and calculation to find number of secondary turns

Correct Answer: B deflect the electron beam horizontally.

The x-plate in a cathode ray oscilloscope (CRO) is specifically designed to deflect the electron beam horizontally across the screen. This horizontal deflection creates the time base or sweep function, allowing waveforms to be displayed as voltage variations over time. The y-plates are responsible for vertical deflection based on the input signal amplitude.

MARK SCHEME:

[M1]: Identifying that the x-plate deflects the electron beam horizontally

Nuclear fission is the process in which a heavy atomic nucleus splits into two or more lighter nuclei, accompanied by the release of energy and neutrons.

This process typically occurs when a heavy nucleus (such as uranium-235 or plutonium-239) absorbs a neutron and becomes unstable. The nucleus then breaks apart into two smaller nuclei of roughly equal mass, along with the emission of additional neutrons and a large amount of energy. This energy is released due to the conversion of a small amount of mass into energy, as described by Einstein's mass-energy equation.

MARK SCHEME:

[M1]: Definition stating that nuclear fission is the splitting of a heavy nucleus into lighter nuclei with energy release

Reading from Graph:

To determine the original mass of the nuclide, we need to find the mass at time t = 0 (the y-intercept of the graph).

From the graph:

At t = 0, the mass = 80 g

This represents the initial mass of the radioactive nuclide before any decay has occurred.

Answer:

MARK SCHEME:

[M1]: Correctly reading the y-intercept from the graph as 80 g

Formula:

where n = tt_1/2

Given:

N₀ = 80 g, t = 6 days, t_1/2 = 2 days

First, calculate the number of half-lives:

Substitution:

Answer:

MARK SCHEME:

[M1]: Correct calculation showing 10 g remains after 6 days

Definition:

The half-life of a nuclide is the time taken for half of the radioactive nuclei in a sample to decay (or disintegrate).

Alternative definition:

The half-life is the time taken for the activity (or count rate) of a radioactive sample to reduce to half its original value.

Key characteristics:

• Half-life is constant for a given nuclide
• It is independent of the initial number of nuclei present
• Half-life varies from fractions of a second to billions of years depending on the nuclide
• After one half-life, 50% of nuclei remain; after two half-lives, 25% remain; after three half-lives, 12.5% remain

MARK SCHEME:

[M1]: Correct definition stating that half-life is the time taken for half the radioactive nuclei to decay OR the time for activity to reduce to half its original value

Analysis of Nuclear Decay Equation:

Given nuclear decay equation:

Conservation Laws:

In nuclear reactions, both mass number (A) and atomic number (Z) must be conserved.

Conservation of Mass Number (A):

Conservation of Atomic Number (Z):

Identification of Particle W:

A particle with mass number 0 and atomic number -1 is a beta-minus particle (electron):

Answer:

MARK SCHEME:

[M1]: Identifies particle W as beta-minus particle/electron with correct notation or description

Formula:

Given:

Sodium has atomic number = 11 (number of protons)

Sodium-24: Mass number = 24

Sodium-23: Mass number = 23

For Sodium-24:

For Sodium-23:

Answer:

MARK SCHEME:

[M1]: Correct number of neutrons for both isotopes (13 for sodium-24 and 12 for sodium-23)

Explanation:

Both sodium-23 and sodium-24 are isotopes of sodium, which means they have the same number of protons (atomic number = 11) but different numbers of neutrons.

Sodium-23:

• Mass number = 23
• Number of protons = 11
• Number of neutrons = 23 - 11 = 12
• This is the most common stable isotope of sodium

Sodium-24:

• Mass number = 24
• Number of protons = 11
• Number of neutrons = 24 - 11 = 13
• This isotope is radioactive with a short half-life

Key Difference:

The additional neutron in sodium-24 makes it heavier and radioactive, while sodium-23 is stable. Both atoms have identical chemical properties since they have the same number of protons and electrons, but they differ in their nuclear properties due to the different number of neutrons.

MARK SCHEME:

[M1]: Identifies that both are isotopes of sodium with same number of protons but different number of neutrons

[M2]: States that sodium-24 has one more neutron than sodium-23 OR gives specific neutron numbers (12 and 13)

Explanation:

The food samples show a measured count rate before treatment with gamma rays due to background radiation.

Background radiation is naturally occurring ionizing radiation that is present everywhere in the environment. It comes from several sources:

• Cosmic rays - high-energy particles from outer space that continuously bombard Earth
• Natural radioactive elements - such as uranium, thorium, and radon present in soil, rocks, and building materials
• Naturally occurring radioactive isotopes - such as carbon-14 and potassium-40 found in all living organisms
• Nuclear weapon testing fallout - residual radioactivity from past atmospheric nuclear tests

The radiation detector used to measure the count rates will detect this background radiation even when no artificial radioactive sources are present. This explains why all three food samples (X, Y, and Z) show count rates of approximately 30-31 counts per minute before any gamma ray treatment.

The slight variations in the background count rates (30, 31, 30 counts per minute) are normal and expected due to the random nature of radioactive decay, which causes natural fluctuations in the measured count rate over time.

MARK SCHEME:

[M1]: Correctly identifies that the count rate before treatment is due to background radiation

Analysis of Food Sample Y:

To determine whether food sample Y becomes radioactive, we need to examine the experimental results and understand the difference between irradiation and activation.

Key Principles:

• When food is exposed to gamma radiation for preservation, the gamma rays pass through the food and kill harmful bacteria

• The food itself does not become radioactive because gamma rays do not cause nuclear reactions that create radioactive isotopes

• For a substance to become radioactive, it must undergo nuclear activation (neutron bombardment), not just gamma irradiation

Conclusion from Results:

Based on the experimental setup where food sample Y was exposed to gamma radiation for food preservation purposes, the sample does NOT become radioactive.

Explanation:

Gamma irradiation used in food preservation involves exposing food to high-energy gamma rays that sterilize the food by destroying microorganisms. However, these gamma rays do not have sufficient energy to cause nuclear reactions in the food atoms that would make them radioactive. The food remains safe to eat and shows no measurable radioactivity after treatment.

Answer:

MARK SCHEME:

[M1]: Correctly states that food sample Y does not become radioactive

[M2]: Provides correct explanation that gamma irradiation does not cause nuclear activation/food atoms remain stable

Answer:

Alternative acceptable answers:

• Sterilization of medical equipment
• Food preservation / Food irradiation
• Industrial radiography / Non-destructive testing
• Thickness gauging in manufacturing
• Nuclear power generation
• Tracer studies in medicine

MARK SCHEME:

[M1]: Any one correct use of gamma radiation stated clearly

Two safety precautions when handling gamma radiation:

1. Use appropriate shielding materials

Lead or thick concrete barriers should be used to absorb gamma radiation and protect the body from exposure, as gamma rays have high penetrating power and can pass through most materials.

2. Maintain safe distance from the radioactive source

Keep as far away as possible from gamma sources when not in use, as radiation intensity decreases with the square of the distance from the source (inverse square law).

Additional acceptable precautions include:

• Limit exposure time to minimize radiation dose received
• Use radiation monitoring badges (dosimeters) to track exposure levels
• Store radioactive sources in lead-lined containers when not in use
• Never point gamma sources directly at people
• Wash hands thoroughly after handling radioactive materials
• Work in well-ventilated areas to avoid inhalation of radioactive particles

MARK SCHEME:

[M1]: One valid safety precaution stated (e.g. use shielding, maintain distance, limit time, use monitoring equipment)

[M2]: Second different valid safety precaution stated

Correct Answer: A ²⁴₁₁Na → ²⁴₁₂Mg + ⁰₋₁He

Analysis of Beta Decay:

In beta-minus decay, a neutron in the nucleus converts to a proton, emitting a beta particle (electron). The beta particle is represented as ⁰₋₁e.

Conservation Laws Check:

For the correct equation ²⁴₁₁Na → ²⁴₁₂Mg + ⁰₋₁e:

Mass number conservation: 24 = 24 + 0 ✓

Atomic number conservation: 11 = 12 + (-1) ✓

Analysis of Other Options:

Option B: Shows gamma emission (γ), not beta decay. Gamma rays have no mass or charge, so atomic number wouldn't change from 11 to 12.

Option C: Mass number changes from 24 to 20, violating conservation of mass number in beta decay.

Option D: Shows mass number increasing from 24 to 25, which is impossible in beta decay, and uses incorrect notation ⁰₋₁He.

Note: The notation in option A uses ⁰₋₁He instead of the standard ⁰₋₁e for the beta particle, but this represents the same particle (electron) with the correct mass and charge numbers.

Answer:

MARK SCHEME:

[M1]: Identifies correct equation showing conservation of mass and atomic numbers in beta decay