An electron (mass m) with an initial velocity is in an electric field . If , its de-Broglie wavelength at time t is given by:
1.
2.
3.
4.
An electron (mass \(m\)) with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}}\)
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. | \(\lambda_0t\) |
An electron is moving with an initial velocity and is in a magnetic field . 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 -particle have the same energy. Then, their de-Broglie wavelengths compare as:
1.
2.
3.
4.
Relativistic corrections become necessary when the expression for the kinetic energy , becomes comparable with , where m is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?
(a)
(b)
(c)
(d)
1. (a, c)
2. (a, d)
3. (c, d)
4. (a, b)
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)
The de-Broglie wavelength of a photon is twice the de-Broglie wavelength of an electron. The speed of the electron is . 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. \(\frac{P_e}{m_ec}=10^{-4}\)
Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency is used to convert 1 kg of ice at to water at . 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)
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 with . 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)
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 \(E_0\). |