Matter waves and the de Broglie relation — practice questions

Question 1 · difficulty L1 · recall

The de Broglie wavelength of a particle with momentum p is

• A. λ=hp
• B. λ=p/h
• C. λ=h/p
• D. λ=hc/p

Question 2 · difficulty L1 · understanding

For a nonrelativistic particle of mass m and speed v, de Broglie wavelength is

• A. hmv
• B. mv/h
• C. hv/m
• D. h/(mv)

Question 3 · difficulty L2 · understanding

Electron diffraction provides evidence for

• A. the wave nature of matter
• B. only classical particle trajectories
• C. absence of electron momentum
• D. magnetic monopoles

Question 4 · difficulty L2 · application

If a particle's momentum doubles, its de Broglie wavelength

• A. doubles
• B. halves
• C. quadruples
• D. stays unchanged

Question 5 · difficulty L2 · understanding

An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20 \%$. The de Broglie wavelength of electron in the medium is $\alpha \lambda_0$, where $\lambda_0$ is its de Broglie wavelength in free space. The value of $\alpha$ is $\_\_\_\_$ .

• A. 1.20
• B. 1.0
• C. 1.25
• D. 0.75

Question 6 · difficulty L2 · understanding

The de Broglie wavelength associated with an electron accelerated through a potential difference V is $\lambda_{\mathrm{e}}$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is $\lambda_{\mathrm{p}}$. If their corresponding masses are $m_{\mathrm{e}}$ and $m_{\mathrm{p}}$, respectively, then the ratio of their de Broglie wavelengths $\left(\frac{\lambda_e}{\lambda_p}\right)$ is $\_\_\_\_$ .

• A. $$\text { } \sqrt{\frac{m_p}{m_e}}$$
• B. $$\sqrt{\frac{m_e}{m_p}}$$
• C. $$\frac{m_p}{m_e}$$
• D. $$\left(\frac{m_p}{m_e}\right)^2$$

Question 7 · difficulty L2 · understanding

An electron with mass ' m ' with an initial velocity $(\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0>0\right)$ enters a magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{j}$. If the initial de-Broglie wavelength at $\mathrm{t}=0$ is $\lambda_0$ then its value after time ' t ' would be :

• A. $\frac{\lambda_0}{\sqrt{1-\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}$
• B. $\lambda_0$
• C. $\lambda_0 \sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}$
• D. $\frac{\lambda_0}{\sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}$

Question 8 · difficulty L2 · understanding

A sub-atomic particle of mass $10^{-30} \mathrm{~kg}$ is moving with a velocity $2.21 \times 10^6 \mathrm{~m} / \mathrm{s}$. Under the matter wave consideration, the particle will behave closely like $\qquad$ $\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)$

• A. X-rays
• B. Infra-red radiation
• C. Gamma rays
• D. Visible radiation

Question 9 · difficulty L2 · understanding

A proton and an electron have the same de Broglie wavelength. If $$\mathrm{K}_{\mathrm{p}}$$ and $$\mathrm{K}_{\mathrm{e}}$$ be the kinetic energies of proton and electron respectively, then choose the correct relation :

• A. $$\mathrm{K_p>K_e}$$
• B. $$\mathrm{K_p=K_e}$$
• C. $$\mathrm{K}_{\mathrm{p}}<\mathrm{K}_{\mathrm{e}}$$
• D. $$\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{e}}{ }^2$$

Question 10 · difficulty L2 · understanding

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume h = 6.63 $$\times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}$$ and $$\mathrm{m}_{\mathrm{p}}=1836$$ times $$\mathrm{m}_{\mathrm{e}}$$ )

• A. $$1: \frac{1}{1836}$$
• B. $$1: \sqrt{1836}$$
• C. $$1: 1836$$
• D. $$1: \frac{1}{\sqrt{1836}}$$