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A particle is dropped from a height \(H.\) The de-Broglie wavelength of the particle as a function of height is proportional to:

1. \(H\)

2. \(H^{1/2}\)

3. \(H^{0}\)

4. \(H^{-1/2}\)

Subtopic: De-broglie Wavelength |

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The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with \(1~\text{MeV}\) energy is nearly:

1. \(1.2~\text{nm}\)

2. \(1.2\times 10^{-3}~\text{nm}\)

3. \(1.2\times 10^{-6}~\text{nm}\)

4. \(1.2\times 10~\text{nm}\)

Subtopic: Einstein's Photoelectric Equation |

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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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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 ${\mathrm{\lambda}}_{1},{\mathrm{\lambda}}_{2}$ 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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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 $0\xb0\mathrm{C}$ to water at $0\xb0\mathrm{C}$. 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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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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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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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) $\mathrm{\lambda}=10\mathrm{nm}$

(b) $\mathrm{\lambda}={10}^{-1}\mathrm{nm}$

(c) $\mathrm{\lambda}={10}^{-4}\mathrm{nm}$

(d) $\mathrm{\lambda}={10}^{-6}\mathrm{nm}$

1. (a, c)

2. (a, d)

3. (c, d)

4. (a, b)

Subtopic: De-broglie Wavelength |

51%

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An electron (mass m) with an initial velocity $\overrightarrow{\mathrm{v}}={\mathrm{v}}_{0}\hat{\mathrm{i}}$ is in an electric field $\overrightarrow{\mathrm{E}}={\mathrm{E}}_{0}\hat{\mathrm{j}}$. 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 |

64%

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An electron (mass \(m\)) with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}}\) $\stackrel{}{\mathrm{}}$

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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