# An electron (mass m) with an initial velocity $\stackrel{\to }{\mathrm{v}}={\mathrm{v}}_{0}\stackrel{^}{\mathrm{i}}$ is in an electric field $\stackrel{\to }{\mathrm{E}}={\mathrm{E}}_{0}\stackrel{^}{\mathrm{j}}$. If ${\mathrm{\lambda }}_{0}=\frac{\mathrm{h}}{{\mathrm{mv}}_{0}}$, its de-Broglie wavelength at time t is given by: 1. ${\mathrm{\lambda }}_{0}$ 2. ${\mathrm{\lambda }}_{0}\sqrt{1+\frac{{\mathrm{e}}^{2}{\mathrm{E}}_{0}^{2}{\mathrm{t}}^{2}}{{\mathrm{m}}^{2}{\mathrm{v}}_{0}^{2}}}$ 3. $\frac{{\mathrm{\lambda }}_{0}}{\sqrt{1+\frac{{\mathrm{e}}^{2}{\mathrm{E}}_{0}^{2}{\mathrm{t}}^{2}}{{\mathrm{m}}^{2}{\mathrm{v}}_{0}^{2}}}}$ 4. $\frac{{\mathrm{\lambda }}_{0}}{\left(1+\frac{{\mathrm{e}}^{2}{\mathrm{E}}_{0}^{2}{\mathrm{t}}^{2}}{{\mathrm{m}}^{2}{\mathrm{v}}_{0}^{2}}\right)}$

Subtopic:  De-broglie Wavelength |
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An electron (mass $$m$$) with an initial velocity $$\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}}$$ $\stackrel{}{\mathrm{}}$($$\mathrm{v}_0>0$$is in an electric field $$\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{i}}$$$\left({\mathrm{}}_{}$$$E_o$$=constant$$>0$$). Its de-Broglie wavelength at time $$t$$ is given by:

 1 $$\frac{\lambda_0}{\left(1+\frac{e E_0}{m} \frac{t}{\mathrm{v}_0}\right)}$$ 2 $$\lambda_0\left(1+\frac{e E_0 t}{m \mathrm{v}_0}\right)$$ 3 $$\lambda_0$$ 4 $$\lambda_0t$$
Subtopic:  De-broglie Wavelength |
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An electron is moving with an initial velocity $\stackrel{\to }{\mathrm{v}}={\mathrm{v}}_{0}\stackrel{^}{\mathrm{i}}$ and is in a magnetic field $\stackrel{\to }{\mathrm{B}}={\mathrm{B}}_{0}\stackrel{^}{\mathrm{j}}$. Then, its de-Broglie wavelength:

1. remains constant

2. increases with time

3. decreases with time

4. increases and decreases periodically

Subtopic:  De-broglie Wavelength |
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A proton, a neutron, an electron and an $\mathrm{\alpha }$-particle have the same energy. Then, their de-Broglie wavelengths compare as:

1. ${\mathrm{\lambda }}_{\mathrm{p}}={\mathrm{\lambda }}_{\mathrm{n}}>{\mathrm{\lambda }}_{\mathrm{e}}>{\mathrm{\lambda }}_{\mathrm{\alpha }}$

2. ${\mathrm{\lambda }}_{\mathrm{\alpha }}<{\mathrm{\lambda }}_{\mathrm{p}}={\mathrm{\lambda }}_{\mathrm{n}}<{\mathrm{\lambda }}_{\mathrm{e}}$

3. ${\mathrm{\lambda }}_{\mathrm{e}}<{\mathrm{\lambda }}_{\mathrm{p}}={\mathrm{\lambda }}_{\mathrm{n}}>{\mathrm{\lambda }}_{\mathrm{\alpha }}$

4. ${\mathrm{\lambda }}_{\mathrm{e}}={\mathrm{\lambda }}_{\mathrm{p}}={\mathrm{\lambda }}_{\mathrm{n}}={\mathrm{\lambda }}_{\mathrm{\alpha }}$

Subtopic:  De-broglie Wavelength |
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Relativistic corrections become necessary when the expression for the kinetic energy $\frac{1}{2}{\mathrm{mv}}^{2}$, becomes comparable with ${\mathrm{mc}}^{2}$, where m is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?

(a)
(b)
(c)
(d)

1. (a, c)

2. (a, d)

3. (c, d)

4. (a, b)

Subtopic:  De-broglie Wavelength |
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Two particles $$A_1$$ and $$A_2$$ of masses $${m_1},m_2$$  $$({m_1>m_2})$$ have the same de-Broglie wavelength. Then:

 (a) their momenta (magnitude) are the same (b) their energies are the same (c) energy of $$A_1$$ is less than the energy of $$A_2$$ (d) energy of $$A_1$$ is more than the energy of $$A_2$$

1. (b), (c)
2. (a), (c)
3. (c), (d)
4. (b), (d)

Subtopic:  De-broglie Wavelength |
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The de-Broglie wavelength of a photon is twice the de-Broglie wavelength of an electron. The speed of the electron is ${\mathrm{v}}_{\mathrm{e}}=\frac{\mathrm{c}}{100}$. Then,

1. $$\frac{E_e}{E_p}=10^{-4}$$

2. $$\frac{E_e}{E_p}=10^{-2}$$

3. $$\frac{P_e}{m_ec}=10^{-2}$$

4. $$\frac{P_e}{m_ec}=10^{-4}$$

Subtopic:  De-broglie Wavelength |
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Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency $\mathrm{\nu }$ is used to convert 1 kg of ice at $0°\mathrm{C}$ to water at $0°\mathrm{C}$. Then, the time T taken for the conversion:

 (a) decreases with increasing n, with  ν fixed (b) decreases with n fixed,  ν increasing (c) remains constant with n and  ν changing such that n ν =constant (d) increases when the product n ν increases

1. (b, d)
2. (a, c, d)
3. (a, d)
4. (a, b, c)

Subtopic:  Particle Nature of Light |
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A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de-Broglie wavelength of the particle varies cyclically between two values  with ${\mathrm{\lambda }}_{1}>{\mathrm{\lambda }}_{2}$. Which of the following statement/s is/are true?

 (a) The particle could be moving in a circular orbit with origin as the centre. (b) The particle could be moving in an elliptic orbit with origin as its focus. (c) When the de-Broglie wavelength is  λ 1 , the particle is nearer the origin than when its value is  λ 2 . (d) When the de-Broglie wavelength is  λ 2 , the particle is nearer the origin than when its value is  λ 1 .

1. (b, d)

2. (a, c)

3. (b, c, d)

4. (a, c, d)

Subtopic:  De-broglie Wavelength |
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Consider a beam of electrons (each electron with energy $$E_0$$) incident on a metal surface kept in an evacuated chamber. Then:

 1 no electrons will be emitted as only photons can emit electrons. 2 electrons can be emitted but all with energy, $$E_0$$${\mathrm{}}_{}$. 3 electrons can be emitted with any energy, with a maximum of $$\mathrm{E}_0-\phi$$ ($$\phi$$ is the work function). 4 electrons can be emitted with any energy, with a maximum $$E_0$$.
Subtopic:  Electron Emission |
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