Q. No.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. | \(\lambda_0t\) |
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
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. \(\lambda_e =\lambda_p = \lambda_n=\lambda_\alpha\)
| (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)
| (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)
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) | 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)
| (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)
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 \(\mathrm{E}_0-\phi\) (\(\phi\) is the work function). |
| 4. | electrons can be emitted with any energy, with a maximum \(E_0\). |
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