IB Physics HL Theme E: Nuclear and quantum physics 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 choiceMedium1 mark

The schematic shows two spherical nuclei. Assume that all nucleons have the same mass. Each option gives $R_X/R_Y$ and $\rho_X/\rho_Y$ respectively. Which row is correct?

Show answer and explanation

Answer: C. The nuclear radius relation is $R=R_0A^{1/3}$ From the figure, $R_X/R_Y=(8/64)^{1/3}=1/2$ The mass ratio is $1/8$ and the spherical volume ratio is $(1/2)^3=1/8$ so $\rho_X/\rho_Y=(1/8)/(1/8)=1$

A: uses the mass ratio as the density ratio, omitting the volume comparison.
B: reverses the radius ratio, although its density ratio is unity.
D: treats the masses as equal and uses the inverse volume ratio, giving $8$
Remember: nuclear mass and volume both scale with nucleon number, so nuclear density is constant.

Question 2

Paper 2Medium7 marks

A gas is examined using an emission spectrum and an absorption spectrum. The absorption spectrum is recorded after continuous light passes through a cooler sample of the same gas. Figure 1 shows measured relative intensities for both spectra.

For calculations, use $h=6.63\times10^{-34}\,\text{J s}$ and $c=3.00\times10^8\,\text{m s}^{-1}$

(a)

Read Figure 1 to state the wavelengths of the shortest- and longest-wavelength emission lines. Give your answers in nm.

[2]

(b)

Determine the energy of a photon in the longest-wavelength emission line. Give your answer in J.

[2]

(c)

Explain what the matching emission and absorption line positions indicate about atomic energy levels.

[2]

(d)

A nucleus of the element contains 12 protons and 13 neutrons. Write its nuclear notation, using $X$ for the chemical symbol.

[1]

Question 3

Multiple choiceMedium1 mark

Two non-relativistic particles, X and Y, have masses $m$ and $2m$ and speeds $v$ and $3v$ respectively. Which row gives the momentum ratio $p_Y/p_X$ and de Broglie wavelength ratio $\lambda_Y/\lambda_X$

Show answer and explanation

Answer: A. For non-relativistic particles, $p=mv$ so $p_Y/p_X=(2m)(3v)/(mv)=6$ Since $\lambda=h/p$ $\lambda_Y/\lambda_X=p_X/p_Y=1/6$

B: treats wavelength as directly proportional to momentum. C: omits the mass difference when comparing momenta, giving $p_Y/p_X=3$ D: reverses the ratios, giving $p_X/p_Y$ and $\lambda_X/\lambda_Y$ instead.

Remember: de Broglie wavelength is inversely proportional to momentum.

Question 4

Multiple choiceMedium1 mark

A fusion event in a star is represented below. The labels give the total rest masses before and after fusion. What fraction of the initial rest energy is released?

Show answer and explanation

Answer: B. The energy released is the decrease in rest energy, $E_{\rm rel}=(M_i-M_f)c^2$ The initial rest energy is $E_i=M_i c^2$ so $\dfrac{E_{\rm rel}}{E_i}=\dfrac{(M_i-M_f)c^2}{M_i c^2}=\dfrac{M_i-M_f}{M_i}$

A: divides the mass defect by the final mass, not the initial mass.
C: gives the fraction of the initial rest energy that remains as product rest energy.
D: takes the reciprocal of the required fraction.
Remember: the energy released in fusion comes from the decrease in rest energy.

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