Q. No.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. \(H^{-1/2}\)
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. \(1.2\times 10~\text{nm}\)
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, \(E_0\) |
| 3. | electrons can be emitted with any energy, with a maximum of \({E}_0-\phi\) (\(\phi\) is the work function). |
| 4. | electrons can be emitted with any energy, with a maximum \(E_0\). |
| (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)
| (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) |
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. \(\dfrac{P_e}{m_ec}=10^{-4}\)
| (a) | Their momenta (magnitude) are the same. |
| (b) | Their energies are the same. |
| (c) | The energy of \(A_1\) is less than the energy of \(A_2.\) |
| (d) | The energy of \(A_1\) is more than the energy of \(A_2.\) |
Choose the correct option from the given ones:
| 1. | (b), (c) only |
| 2. | (a), (c) only |
| 3. | (c), (d) only |
| 4. | (b), (d) only |
| (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)
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. \(\dfrac{\lambda_{0}}{\left(1 + \dfrac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}\right)}\)
| 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. | \(\lambda_0t\) |
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