Q. No.An electron of mass \(m\) with an initial velocity \(\overrightarrow v= v_0\hat i\)\( ( v_o > 0 ) \) enters in an electric field \(\overrightarrow E = -E_0 \hat i\) \((E_0 = \text{constant}>0)\) at \(t=0.\) If \(\lambda_0,\)
1. \(\frac{\lambda_0}{\left(1+ \frac{eE_0}{mv_0}t\right)}\)
2. \(\lambda_0\left(1+ \frac{eE_0}{mv_0}t\right)\)
3. \(\lambda_0 t\)
4. \(\lambda_0\)
1. \(\frac{\lambda_0}{\left(1+ \frac{eE_0}{mv_0}t\right)}\)
2. \(\lambda_0\left(1+ \frac{eE_0}{mv_0}t\right)\)
3. \(\lambda_0 t\)
4. \(\lambda_0\)
When the light of frequency \(2\nu_0\) (where \(\nu_0\) is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is \(v_1.\) When the frequency of the incident radiation is increased to \(5\nu_0,\) the maximum velocity of electrons emitted from the same plate is \(v_2.\) What will be the ratio of \(v_1\) to \(v_2?\)
| 1. | \(1:2\) | 2. | \(1:4\) |
| 3. | \(4:1\) | 4. | \(2:1\) |
1. \(5\lambda\)
2. \(\frac{5}{2} \lambda\)
3. \(3\lambda\)
4. \(4\lambda\)
A photoelectric surface is illuminated successively by the monochromatic light of wavelength \(\lambda\) and \(\frac{\lambda}{2}\). If the maximum kinetic energy of the emitted photoelectrons in the second case is \(3\) times that in the first case, the work function of the surface of the mineral is:
[\(h\) = Plank’s constant, \(c\) = speed of light]
1. \(\dfrac{hc}{2\lambda}\)
2. \(\dfrac{hc}{\lambda}\)
3. \(\dfrac{2hc}{\lambda}\)
4. \(\dfrac{hc}{3\lambda}\)
Light of wavelength \(500~\text{nm}\) is incident on metal with work function \(2.28~\text{eV}\). The de-Broglie wavelength of the emitted electron is:
| 1. | \(< 2.8\times 10^{-10}~\text{m} \) | 2. | \(< 2.8\times 10^{-9}~\text{m}\) |
| 3. | \(\geq 2.8\times 10^{-9}~\text{m}\) | 4. | \(\leq 2.8\times 10^{-12}~\text{m}\) |
Radiation of energy \(E\) falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:
(\(c\) = velocity of light)
1. \(E \over c\)
2. \(2E \over c\)
3. \(2E \over c^2\)
4. \(E \over c^2\)
| 1. | \(6\lambda\) | 2. | \(4\lambda\) |
| 3. | \(\dfrac{\lambda}{4}\) | 4. | \(\dfrac{\lambda}{6}\) |
Which of the following figures represent the variation of the particle momentum and the associated de-Broglie wavelength?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
When the energy of the incident radiation is increased by \(20\%\), the kinetic energy of the photoelectrons emitted from a metal surface increases from \(0.5~\text{eV}\) to \(0.8~\text{eV}\). The work function of the metal is:
1. \(0.65~\text{eV}\)
2. \(1.0~\text{eV}\)
3. \(1.3~\text{eV}\)
4. \(1.5~\text{eV}\)
If the kinetic energy of the particle is increased to \(16\) times its previous value, the percentage change in the de-Broglie wavelength of the particle is:
1. \(25\)
2. \(75\)
3. \(60\)
4. \(50\)
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