Matter Waves

Q. The speed of an electron having a wavelength of ${10}^{-10}m$ is

1. $7.25\times {10}^{6}m/s$
2. $6.26\times {10}^{6}m/s$
3. $5.25\times {10}^{6}m/s$
4. $4.24\times {10}^{6}m/s$

Q. A particle of mass M at rest decays into two particles of masses $m_1$ and $m_2$, having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles, $\frac{{\lambda }_1}{{\lambda }_2}$ is

1. $\frac{m_1}{m_2}$
2. $\frac{m_2}{m_1}$
3. $1.0$
4. $\frac{\sqrt{m_2}}{\sqrt{m_1}}$

Q.

If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor

1. $\frac{1}{\sqrt{2}}$

2. $\sqrt{2}$

3. $\frac{1}{2}$

4. $2$

Q. The de-Broglie wavelength of an electron having 80eV of energy is nearly $(leV=1.6\times {10}^{-19}J$ Mass of electron $9\times {10}^{-31}kg$ and Plank's constant $6.6\times {10}^{-34}Jsec)$

1. $0.14\stackrel{\circ }{A}$
2. $14\stackrel{\circ }{A}$
3. $140\stackrel{\circ }{A}$
4. $1.4\stackrel{\circ }{A}$

Q.

The momentum of a photon in an X-ray beam of ${10}^{-10}$ metre wavelength is

1. $1.5\times {10}^{-23}kg-m/sec$

2. $6.6\times {10}^{-24}kg-m/sec$

3. $6.6\times {10}^{-44}kg-m/sec$

4. $2.2\times {10}^{-52}kg-m/sec$

Q.

A photon, an electron and a uranium nucleus all have the same wavelength. The one with the most energy

1. Is the photon

2. Is the electron

3. Is the uranium nucleus

4. Depends upon the wavelength and the properties of the particle.

Q.

In which of the following situations the heavier of the two particles has smaller de Broglie wavelength? The two particles

1. move with the same speed

2. move with the same linear momentum

3. move with the same kinetic energy

4. have fallen through the same height

Q.

Which of one is correct

1. $E^2=p^2{c}^2$

2. $E^2=p^{2}c$

3. $E^2=p{c}^2$

4. $E^2=\frac{p^2}{c^2}$

Q.

Which of one is correct

1. $E^2=p^2{c}^2$

2. $E^2=p^{2}c$

3. $E^2=p{c}^2$

4. $E^2=\frac{p^2}{c^2}$

Q. An electron, an $\alpha$- particle and a proton have the same K.E. Which of these particles has the shortest de Broglie wavelength?

1. electron
2. proton
3. $\alpha$- particle
4. electron, proton

Q.

The momentum of the photon of wavelength $5000\dot{A}$ will be

1. $1.3\times {10}^{-27}kg-m/sec$

2. $1.3\times {10}^{-28}kg-m/sec$

3. $4\times {10}^{29}kg-m/sec$

4. $4\times {10}^{-18}kg-m/sec$

Q. If we consider electrons and photons of the same wavelength, then they will have the same

1. velocity
2. angular momentum
3. energy
4. momentum

Q.

If the momentum of a photon is p, then its frequency is
Where m is the rest mass of the photon

1. ph/c

2. pc/h

3. mh/c

4. mc/h

Q.

The momentum of a photon is $2\times {10}^{-16}gm-cm/sec$. Its energy is

1. $0.61\times {10}^{-26}erg$

2. $2.0\times {10}^{-26}erg$

3. $6\times {10}^{-6}erg$

4. $6\times {10}^{-8}erg$

Q.

The momentum of a photon of energy hv will be

1. $hcv$

2. $\frac{hv}{c}$

3. $hvc$

4. $\frac{h}{v}$

Q. An electron, an $\alpha$- particle and a proton have the same K.E. Which of these particles has the shortest de Broglie wavelength?

1. electron
2. proton
3. $\alpha$- particle
4. electron, proton

Q.

If a photon has velocity c and frequency v, then which of following represents its wavelength

1. $\frac{hc}{E}$

2. $\frac{hv}{c}$

3. $\frac{hv}{c^2}$

4. $hv$

Q. The ratio of de-Broglie wavelengths of molecules of hydrogen and helium which are at temperature ${27}^{\circ }C$ and ${127}^{\circ }C$ respectively is

1. $\frac{1}{2}$
2. $\sqrt{\frac{3}{8}}$
3. $\sqrt{\frac{8}{3}}$
4. 1

Q.

The kinetic energy of an electron with de-Broglie wavelength of 0.3 nanometer is

1. 0.168 eV

2. 16.8 eV

3. 1.68 eV

4. 2.5 eV

Q. Ultraviolet light of wavelength $\lambda =200\text{nm}$ is used in an experiment on photoelectric effect with caesium ($\varphi =1.8\text{eV}$). Find De-Broglie wavelength of photo electron with maximum kinetic energy.

1. $\frac{4}{7}\times {10}^{-9}m$
2. 
   $\frac{28}{5}\times {10}^{-9}m$
3. $\frac{19}{7}\times {10}^{-9}m$
4. $\frac{2}{7}\times {10}^{-9}m$

Q. The de Broglie wavelength of electron changes by $x$ % when it is shifted from n = 1 to n = 4. The value of $x$ % is

1. 50%
2. 300%
3. 200%
4. 100%

Q. The de-Broglie wavelength of a particle accelerated with a p.d of 150 V is ${10}^{-10}m$. If it is accelerated with a p.d of 600 V, its wavelength will be

1. $0.25\stackrel{\circ }{A}$
2. $0.5\stackrel{\circ }{A}$
3. $1.5\stackrel{\circ }{A}$
4. $2\stackrel{\circ }{A}$

Q. A particle of mass $M$ at rest decays into two particles of masses $m_1$ and $m_2$, having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles, ${\lambda }_1/{\lambda }_2$ is

1. $1.0$
2. $\sqrt{m_2}/\sqrt{m_1}$
3. $m_2/m_1$
4. $m_1/m_2$

Q.

For moving ball of cricket, the correct statement about de-Broglie wavelength is

1. It is not applicable for such big particle

2. $\frac{h}{\sqrt{2mE}}$

3. $\sqrt{\frac{h}{2mE}}$

4. $\frac{h}{2mE}$

Q.

The momentum of a photon is $2\times {10}^{-16}gm-cm/sec$. Its energy is

1. $0.61\times {10}^{-26}erg$

2. $2.0\times {10}^{-26}erg$

3. $6\times {10}^{-6}erg$

4. $6\times {10}^{-8}erg$

Q. The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ (Kelvin) and mass $m$, is

1. $\frac{2h}{\sqrt{mkT}}$
2. $\frac{h}{\sqrt{mkT}}$
3. $\frac{h}{\sqrt{3mkT}}$
4. $\frac{2h}{\sqrt{3mkT}}$

Q.

The de-Broglie wavelength of a neutron at ${27}^{\circ }C$ is $\lambda$ . What will be its wavelength at ${927}^{\circ }C$

1. $\frac{\lambda }{2}$

2. $\frac{\lambda }{3}$

3. $\frac{\lambda }{4}$

4. $\frac{\lambda }{9}$

Q. A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is $1.813\times {10}^{-4}.$ Calculate the particle’s mass. (Given mass of electron is $9.109\times {10}^{-31}kg)$

1. $1.675\times {10}^{-27}kg$
2. $9.109\times {10}^{-31}kg$
3. $9.109\times {10}^{-27}kg$
4. $1.675\times {10}^{-31}kg$

Q. What is the ratio of de Brogile wavelength of deuteron moving with a velocity 2 v and $\alpha$ -particle moving with velocity v ?

1. 1:1
2. 1:2
3. 1:4
4. 4:1

Q. If the kinetic energy of a free electron doubles, its de-Broglie wave length changes by the factor of

1. $\sqrt{2}$
2. $2$
3. $\frac{1}{2}$
4. $\frac{1}{\sqrt{2}}$