Matter Waves

Q. An electron is accelerated through a potential difference of $10,000V$. Its de Broglie wavelength is (nearly) $\left(m_e=9\times {10}^{-31}kg\right)$

1. $12.2\times {10}^{-13}m$
2. $12.2\times {10}^{-12}m$
3. $12.2\times {10}^{-14}m$
4. $12.2nm$

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 $E_1,E_2$ and $E_3$ respectively represent the kinetic energies of an electron, an $\alpha$-particle and a proton each having same de-Broglie’s wavelength, then

1. $E_1>E_2>E_3$
2. $E_2>E_3>E_1$
3. $E_1>E_3>E_2$
4. $E_1=E_2=E_3$

Q.

Figure shows a square plate of uniform thickness and side length $\sqrt{2}$m. One fourth of the plate is removed as indicated. The distance of centre of mass of the remaining portion from the centre of the original square plate is

1. 1/3m

2. 1/2 m

3. 1/6 m

4. 1/8m

Q. The de-Broglie wavelength associated with a hydrogen atom moving with a thermal velocity of 3 km/s will be

1. $1\stackrel{\circ }{A}$
2. $0.66\stackrel{\circ }{A}$
3. $6.6\stackrel{\circ }{A}$
4. $66\stackrel{\circ }{A}$

Q.

The wave nature of electrons is used in which of the following devices?

1. Tokamak

2. Aeroplane

3. Photocell

4. Electron microscope

Q.

The de-Broglie wavelength associated with the particle of mass m moving with velocity v is

1. h/mv

2. mv/h

3. mh/v

4. m/hv

Q.

Wave is associated with matter

1. When it is stationary

2. When it is in motion with the velocity of light only

3. When it is in motion with any velocity

4. None of the above

Q. de-Broglie wavelength of a body of mass m and kinetic energy E is given by

1. $\lambda =\frac{h}{mE}$
2. $\lambda =\frac{\sqrt{2mE}}{h}$
3. $\lambda =\frac{h}{2mE}$
4. $\lambda =\frac{h}{\sqrt{2mE}}$

Q.

Wave is associated with matter

1. When it is stationary

2. When it is in motion with the velocity of light only

3. When it is in motion with any velocity

4. None of the above

Q.

An electron and proton have the same de-Broglie wavelength. Then the kinetic energy of the electron is

1. Zero

2. Infinity

3. Equal to the kinetic energy of the proton

4. Greater than the kinetic energy of the proton

Q.

The wavelength associated with an electron accelerated through a potential difference of 100 V is nearly

1. $100\dot{A}$

2. $123\dot{A}$

3. $1.23\dot{A}$

4. $0.123\dot{A}$

Q.

A proton and an $\alpha$ -particle are accelerated through a potential difference of 100 V. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is

1. $\sqrt{2}:1$

2. $2:1$

3. $2\sqrt{2}:1$

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

Q. The velocity of photon is proportional to (where vis frequency)

1. $\frac{v^2}{2}$
2. $\frac{1}{\sqrt{v}}$
3. $\sqrt{V}$
4. $v$

Q.

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

Q. If the electron has same momentum as that of a photon of wavelength $5200\stackrel{\circ }{A}$, then the velocity of electron in m /sec is given by

1. ${10}^3$
2. $1.4\times {10}^3$
3. $7\times {10}^{-5}$
4. $7.2\times {10}^6$

Q.

The de Broglie wavelength of an electron moving with a velocity 0f $1.5X{10}^8$ m/s is equal to that of a photon. The ratio of kinetic energy of that electron to the photon is.

[IIT JEE 2004]

1. 2

2. 4

3. 1/2

4. 1/4

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. An electron and a photon have same wavelength. It p is the momentum of electron and E the energy of photon. The magnitude of p/ E in S.I. unit is

1. $3.0\times {10}^8$
2. $3.33\times {10}^{-9}$
3. $9.1\times {10}^{-31}$
4. $6.64\times {10}^{-34}$

Q.

The rest mass of the photon is

1. 0

2. $\infty$

3. Between 0 and $\infty$

4. Equal to that of an electron

Q. de-Broglie wavelength of a body of mass m and kinetic energy E is given by

1. $\lambda =\frac{h}{mE}$
2. $\lambda =\frac{\sqrt{2mE}}{h}$
3. $\lambda =\frac{h}{2mE}$
4. $\lambda =\frac{h}{\sqrt{2mE}}$

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. The kinetic energy of an electron is 5 eV. Calculate the de-Broglie wavelength associated with it $(h=6.6\times {10}^{-34}Js,me=9.1\times {10}^{-31}kg)$

1. $5.47\dot{A}$
2. $10.9\dot{A}$
3. $2.7\dot{A}$
4. None of these

Q.

A proton and an electron are accelerated by the same potential difference. Let${\lambda }_e$ and ${\lambda }_p$ denote the de Broglie wavelengths of the electron and the proton respectively.

1. ${\lambda }_e={\lambda }_p$

2. ${\lambda }_e<{\lambda }_p$

3. ${\lambda }_e>{\lambda }_p$

4. The relation between ${\lambda }_{e}and{\lambda }_p$depends on the accelerating potential difference

Q. The heavier of the two particles has smaller de Broglie wavelength if the two particles move with same speed.

1. True
2. False

Q. The ratio of de Broglie wavelength of an $\alpha$- particle and a proton of same kinetic energy is

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

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 ratio of de-Broglie wavelength of a $\alpha$ -particle to that of a proton when they are subjected to the same magnetic field and their radii in the magnetic field are equal (assume the field induction vector $\overrightarrow{B}$ is perpendicular to the velocity vectors of the $\alpha$ -particle and the proton) is

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

Q.

What is the momentum of a photon having frequency $1.5\times {10}^{13}Hz$

1. $3.3\times {10}^{-29}kgm/s$
   

2. $3.3\times {10}^{-34}kgm/s$

3. $6.6\times {10}^{-34}kgm/s$

4. $6.6\times {10}^{-30}kgm/s$

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