A proton, a neutron, an electron and an $$\alpha\text-$$particle have the same energy. Then, their de-Broglie wavelengths compare as: 1. $$\lambda_p= \lambda_n>\lambda_e>\lambda_\alpha$$ 2. $$\lambda_\alpha <\lambda_p = \lambda_n<\lambda_e$$ 3. $$\lambda_e<\lambda_p=\lambda_n>\lambda_\alpha$$ 4. $$\lambda_e =\lambda_p = \lambda_n=\lambda_\alpha$$

Subtopic:  De-broglie Wavelength |
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An electron is moving with an initial velocity $$\vec v= v_0 \hat i$$ and is in a magnetic field $$\vec B = B_0 \hat j .$$ 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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An electron (mass $$m$$) with an initial velocity $$\vec{v}={v}_0 \hat{i}$$ $\stackrel{}{\mathrm{}}$$$({v}_0>0)$$ is in an electric field $$\vec{E}=-{E}_0 \hat{i}$$$\left({\mathrm{}}_{}$$$E_0$$ = constant $$>0$$). Its de-Broglie wavelength at time $$t$$ is given by:
 1 $$\dfrac{\lambda_0}{\left(1+\dfrac{e E_0}{m} \dfrac{t}{{v}_0}\right)}$$ 2 $$\lambda_0\left(1+\dfrac{e E_0 t}{m {v}_0}\right)$$ 3 $$\lambda_0$$ 4 $$\lambda_0t$$
Subtopic:  De-broglie Wavelength |
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An electron (mass $$m$$) with an initial velocity $$\overset{\rightarrow}{v} = v_{0} \hat{i}$$ is in an electric field $$\overset{\rightarrow}{E} = E_{0} \hat{j}$$. If $$\lambda_{0} = \dfrac{h}{ {mv}_0}$$, its de-Broglie wavelength at time $$t$$ is given by:

1. $$\lambda_0$$

2. $$\lambda_{0} \sqrt{1 + \dfrac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}$$

3. $$\dfrac{\lambda_{0}}{\sqrt{1 + \dfrac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}$$

4. $$\dfrac{\lambda_{0}}{\left(1 + \dfrac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}\right)}$$

Subtopic:  De-broglie Wavelength |
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Relativistic corrections become necessary when the expression for the kinetic energy $$\dfrac{1}{2} mv^{2}$$, becomes comparable with $$mc^{2}$$, where $$m$$ is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?
 (a) $$\lambda = 10~\text{nm}$$ (b) $$\lambda = 10^{-1}~\text{nm}$$ (c) $$\lambda = 10^{- 4}~\text{nm}$$ (d) $$\lambda = 10^{- 6}~\text{nm}$$

Choose the correct option:
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 $$A_2$$.

Choose the correct option:
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 $$v_e = \dfrac c {100}$$. Then,

1. $$\dfrac{E_e}{E_p}=10^{-4}$$
2. $$\dfrac{E_e}{E_p}=10^{-2}$$
3. $$\dfrac{P_e}{m_ec}=10^{-2}$$
4. $$\dfrac{P_e}{m_ec}=10^{-4}$$

Subtopic:  De-broglie Wavelength |
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Photons absorbed in matter are converted to heat. A source emitting $$n$$ photon/sec of frequency $$\nu$$ is used to convert $$1$$ kg of ice at $$0^{\circ}\text{C}$$ to water at $$0^{\circ}\text{C}$$. Then, the time $$T$$ taken for the conversion:
 (a) decreases with increasing $$n$$, with $$\nu$$ fixed (b) decreases with $$n$$ fixed, $$\nu$$ increasing (c) remains constant with $$n$$ and $$\nu$$ changing such that $$n\nu=$$ constant (d) increases when the product $$n\nu$$ increases

Choose the correct option:
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 $$\lambda_{1} , \lambda_{2}$$ with $$\lambda_{1} > \lambda_{2}$$. 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 $$λ_1$$.

Choose the correct option:
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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