Which among the following verified the wave nature of electrons experimentally?

1. De-Broglie 

2. Hertz

3. Einstein 

4. Davisson and Germer 

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:

Consider the figure given below. Suppose the voltage applied to A is increased. The diffracted beam will have the maximum at a value of $\mathrm{\theta }$ that
                  
1. will be larger than the earlier value

2. will be the same as the earlier value

3. will be less than the earlier value 

4. will depend on the target

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 ${\mathrm{\lambda }}_1, {\mathrm{\lambda }}_2$ with ${\mathrm{\lambda }}_1>{\mathrm{\lambda }}_2$. Which of the following statement/s is/are true?
 

1. (b, d)

2. (a, c)

3. (b, c, d)

4. (a, c, d)

Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency $\mathrm{\nu }$ is used to convert 1 kg of ice at $0°\mathrm{C}$ to water at $0°\mathrm{C}$. Then, the time T taken for the conversion:
 

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 ${\mathrm{v}}_{\mathrm{e}}=\frac{\mathrm{c}}{100}$. 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:

1. (b), (c)
2. (a), (c)
3. (c), (d)
4. (b), (d)

Relativistic corrections become necessary when the expression for the kinetic energy $\frac{1}{2}{\mathrm{mv}}^2$, becomes comparable with ${\mathrm{mc}}^2$, where m is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?

(a) $\mathrm{\lambda }=10 \mathrm{nm}$
(b) $\mathrm{\lambda }={10}^{-1} \mathrm{nm}$
(c) $\mathrm{\lambda }={10}^{-4} \mathrm{nm}$
(d) $\mathrm{\lambda }={10}^{-6} \mathrm{nm}$

1. (a, c)

2. (a, d)

3. (c, d)

4. (a, b)