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An electron (mass \(m\)) with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}}\) $\stackrel{}{\mathrm{}}$\((\mathrm{v}_0>0)\)

1. | \(\dfrac{\lambda_0}{\left(1+\dfrac{e E_0}{m} \dfrac{t}{\mathrm{v}_0}\right)}\) | 2. | \(\lambda_0\left(1+\dfrac{e E_0 t}{m \mathrm{v}_0}\right)\) |

3. | \(\lambda_0 \) | 4. | \(\lambda_0t\) |

Subtopic: De-broglie Wavelength |

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An electron is moving with an initial velocity $\overrightarrow{\mathrm{v}}={\mathrm{v}}_{0}\hat{\mathrm{i}}$ and is in a magnetic field $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{j}}$. 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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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 \(\dfrac{1}{2} ~\text{mv}^{2}\), becomes comparable with \(\text{mc}^{2}\), 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 $\mathrm{\nu}$ 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 |

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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