IB Physics SL Theme B: The particulate nature of matter questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

Type

Multiple choice Written

Difficulty

Easy Medium Hard

Question 1

Multiple choiceMedium1 mark

A star and the Sun are both modelled as black bodies. The star’s surface area is four times the Sun’s, and its surface temperature is half the Sun’s; both temperatures are absolute, measured in kelvin. What is the star’s luminosity in terms of $L_{\text{sun}}$

Show answer and explanation

Answer: B. For a black body, $L=\sigma AT^4$ Comparing the star with the Sun cancels $\sigma$

\frac{L}{L_{\text{sun}}} =\frac{A}{A_{\text{sun}}}\left(\frac{T}{T_{\text{sun}}}\right)^4 =4\left(\frac12\right)^4 =\frac14.

A: includes the temperature factor but omits the area ratio.
C: uses a square rather than the fourth power of the temperature ratio.
D: includes the area ratio but ignores the temperature dependence.
Remember: for black-body radiation, luminosity depends on the fourth power of absolute temperature.

Question 2

Paper 2Medium11 marks

An observer on Earth measures the apparent brightness of stars A and B shown in Figure 1. Assume that both stars emit uniformly in all directions and that absorption between each star and Earth is negligible.

(a)

State which star has the greater apparent brightness.

[1]

(b)

Determine the ratio $L_B/L_A$

[3]

(c)

Calculate the luminosity of star A.

[2]

(d)

A third star, C, has twice the luminosity of star A and an apparent brightness of $1.2\times10^{-8}\,\mathrm{W\,m^{-2}}$ Determine its distance from Earth.

[3]

(e)

Explain why the apparent brightness of a star decreases as its distance from Earth increases, if its luminosity is unchanged.

[2]

Question 3

Multiple choiceEasy1 mark

A region of Earth is measured twice. Its albedo is unchanged between measurements; the incident and scattered powers are shown. Which row gives the albedo and the scattered power in the later measurement, respectively?

Measurement	Incident power / W	Scattered power / W
First	600	150
Later	1200	—

Show answer and explanation

Answer: D. Albedo is total scattered power divided by total incident power. The first measurement gives $150/600=0.25$ With albedo unchanged, the later scattered power is $0.25\times1200\text{ W}=300\text{ W}$
A: Keeps the initial scattered power instead of scaling it for the increased incident power.
B: Adds scattered power to incident power in the denominator, giving an albedo of $150/(600+150)=0.20$
C: Uses the non-scattered fraction, $1-0.25=0.75$ as the albedo.
Remember: multiply incident power by albedo to find scattered power.

Question 4

Paper 2Easy6 marks

Infrared radiation emitted by Earth’s surface reaches a carbon dioxide molecule in the atmosphere. Figure 1 shows two possible incoming infrared photons and two energy levels of the molecule. The molecule’s natural vibration frequency is $f_0$ In this model, a photon of frequency $f$ has energy $E=hf$

(a)

Using Figure 1, identify which photon can be absorbed by the molecule. Explain your choice using the resonance model and the energy levels.

[3]

(b)

As the molecule returns from $E_1$ to $E_0$ state the frequency of the infrared radiation emitted.

[1]

(c)

State the directions in which the radiation is emitted and explain how this can contribute to the greenhouse effect at Earth’s surface.

[2]

Question 5

Paper 2Medium8 marks

An ideal gas is in a vessel of uniform pressure. Figure 1 shows the gas and a surface $S$ of the vessel. The force shown is the resultant force exerted by the gas on $S$

Use $N_A=6.02\times10^{23}\ \mathrm{mol^{-1}}$ and $R=8.31\ \mathrm{J\,mol^{-1}\,K^{-1}}$ Give answers to three significant figures, except in (d), where give the temperature to the nearest degree Celsius.

(a)

Determine the pressure of the gas.

[2]

(b)

Determine the amount of substance of the gas.

[2]

(c)

Using your answers to (a) and (b), determine the temperature of the gas in kelvin.

[3]

(d)

Express the temperature from (c) in degrees Celsius.

[1]

Question 6

Multiple choiceHard1 mark

A sample of $6.0 \times 10^{23}$ particles of a monatomic gas is initially at $400\ \mathrm{K}$ In a final state, its volume is twice its initial volume, its number density is $3/4$ of the initial value, and its temperature is $2/3$ of the initial value. At both states the gas is sufficiently hot and dilute for the ideal-gas approximation to apply. What is its final internal energy? Take $k_B=1.38 \times 10^{-23}\ \mathrm{J\,K^{-1}}$

Show answer and explanation

Answer: C. The particle-number ratio is the number-density ratio multiplied by the volume ratio: $N_f/N_i=(3/4)(2)=3/2$ Since $U=\frac{3}{2}Nk_BT$ the internal-energy ratio is $(3/2)(2/3)=1$ Thus $U_f=U_i=\frac{3}{2}(6.0\times10^{23})(1.38\times10^{-23})(400)=4.968\times10^3\ \mathrm{J}$ or $5.0\times10^3\ \mathrm{J}$ to two significant figures.
A: treats the number-density ratio as the particle-number ratio, omitting the volume change.
B: accounts for the temperature change but holds the particle number fixed.
D: treats the volume ratio as the particle-number ratio, ignoring the number-density change.
Remember: for an ideal monatomic gas, internal energy depends on particle number and absolute temperature.

Question 7

Paper 2Hard10 marks

A fixed amount of gas is measured in a cylinder with a movable piston. Figure 1 shows the measured pressure–volume states of the gas at two temperatures. The temperatures are in kelvin. $X$ is a further state of the same gas, at an unrecorded temperature. No curves have been fitted to the measurements.

(a)

Describe the pressure–volume relationship indicated by the $300\ \mathrm{K}$ measurements.

[1]

(b)

For the measurements at $V=2.00\ \mathrm{L}$ calculate $PV/T$ at each temperature. Give an appropriate unit.

[2]

(c)

A fixed amount of gas changes from state 1 $(P_1,V_1,T_1)$ to state 2 $(P_2,V_2,T_2)$ Using the empirical pressure–temperature law at constant volume and Boyle’s law at constant temperature, derive a relation between these two states. Temperatures are in kelvin.

[2]

(d)

A controller is expected to switch when the gas reaches $750\ \mathrm{K}$ Use state $X$ and both calibration results from part (b) to estimate the temperature at $X$ and decide whether the controller’s reported temperature is consistent with the measurements. Show your working.

[5]

Question 8

Multiple choiceMedium1 mark

A resistor is tested by increasing the potential difference across it and recording the current. The measured values are plotted.

Which row identifies the resistor’s behaviour and gives the ratio of power dissipated at B to that at A?

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Answer: C. At A, $V/I=2.0/0.40=5.0\ \Omega$ at B, $V/I=5.0/0.80=6.25\ \Omega$ Since the resistance is not constant, the behaviour is non-ohmic. Using $P=IV$ $P_A=0.80\ \mathrm{W}$ and $P_B=4.0\ \mathrm{W}$ so $P_B/P_A=5.0$

A: obtains the power ratio but treats the unequal $V/I$ values as equal, classifying the resistor as ohmic.
B: uses the current ratio, $0.80/0.40=2.0$ as the power ratio and omits the change in potential difference.
D: assumes constant resistance and uses $P\propto I^2$ giving a ratio of $4.0$

Remember: compare $V/I$ to identify ohmic behaviour, and use $P=IV$ for power at each operating point.

Question 9

Multiple choiceMedium1 mark

Two resistors of resistance $R$ and $2R$ are connected in series across an ideal source of potential difference $V$ They are then connected in parallel across an identical ideal source. What is the ratio of the current through the $R$ resistor in the series arrangement to the current through the $2R$ resistor in the parallel arrangement?

Show answer and explanation

Answer: B. In series, the total resistance is $3R$ so the current through $R$ is $V/(3R)$ In parallel, the $2R$ resistor has the full potential difference $V$ so its current is $V/(2R)$ The required ratio is $[V/(3R)]/[V/(2R)]=2/3$ A: uses the current through the $R$ branch in parallel, $V/R$ as the denominator. C: assumes the currents are equal because the source potential differences are equal. D: omits the $2R$ resistor when finding the series resistance, giving a series current of $V/R$ Remember: series current depends on the total resistance, while each parallel branch has the full source potential difference.

Question 10

Paper 2Hard10 marks

Two samples, $X$ and $Y$ have the same length and cross-sectional area. Sample $X$ is a metal; sample $Y$ is an unknown material. Each sample is connected separately to a variable d.c. supply. The potential difference $V$ across the sample and the current $I$ through it are measured at the same temperature.

(a)

Using Figure 1, read the current in each sample when the potential difference is $3.0\ \text{V}$

[2]

(b)

Use the reading for sample $X$ at $3.0\ \text{V}$ to determine its resistance.

[2]

(c)

A third test uses a sample $S$ which is either $X$ or $Y$ It is connected in series with a $50\ \Omega$ resistor to a $6.0\ \text{V}$ supply. The current in the circuit is $60\ \text{mA}$ Use the circuit information and Figure 1 to determine whether $S$ matches $X$ or (Y). Show your reasoning.

[4]

(d)

A student claims that sample $Y$ has no mobile charge carriers because its current is almost zero. Assess this claim using Figure 1 and the idea of mobility of charge carriers.

[2]

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