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. \(H^{-1/2}\)
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)
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. \(\frac{P_e}{m_ec}=10^{-4}\)
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)
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)
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.