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.

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Question 1

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 2

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 3

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 4

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 5

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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