IB Physics HL E.2 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.

Type
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Question 1

Multiple choiceMedium1 mark

Two non-relativistic particles, X and Y, have masses mm and 2m2m and speeds vv and 3v3v respectively. Which row gives the momentum ratio pY/pXp_Y/p_X and de Broglie wavelength ratio λY/λX\lambda_Y/\lambda_X

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Answer: A. For non-relativistic particles, p=mvp=mv so pY/pX=(2m)(3v)/(mv)=6p_Y/p_X=(2m)(3v)/(mv)=6 Since λ=h/p\lambda=h/p λY/λX=pX/pY=1/6\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 pY/pX=3p_Y/p_X=3 D: reverses the ratios, giving pX/pYp_X/p_Y and λX/λY\lambda_X/\lambda_Y instead.

Remember: de Broglie wavelength is inversely proportional to momentum.

Question 2

Paper 2Hard10 marks

A monochromatic X-ray photon scatters from an electron that is initially at rest. Model the interaction as a single photon–electron event, with no energy transferred to the rest of the material. Treat the recoiling electron non-relativistically.

Figure 1 shows the geometry and the measured photon wavelengths. The wavelengths are rounded to the nearest 0.00001 nm0.00001\ \mathrm{nm}

xyincident photon, λi=0.08000 nmscattered photon, λs=0.08243 nm90°Oelectron initially at rest

Use h=6.626×10−34 J sh=6.626\times10^{-34}\ \mathrm{J\,s} c=2.998×108 m s−1c=2.998\times10^8\ \mathrm{m\,s^{-1}} and me=9.11×10−31 kgm_e=9.11\times10^{-31}\ \mathrm{kg}

(a)

Calculate the increase in wavelength of the photon.

[1]
(b)

Calculate the kinetic energy transferred to the electron, in J.

[2]
(c)

Determine the speed and direction of the recoiling electron. Give the direction relative to the positive xx-axis.

[4]
(d)

Calculate the electron’s kinetic energy using your result from (c). Comment on whether this is consistent with your answer to (b), taking the precision of the wavelength measurements into account.

[3]

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