Matter Waves

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

Q.

What is a matter wave?

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

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

Q. When a metal is irradiated by monochromatic light, the maximum kinetic energy of the photo-electrons is 1.2eV. If frequency of the light is increased 50% then maximum kinetic energy of photo-electron is 36eV Evaluate the workfunction of the metal.

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. λ_e= λ_p

2. λ_e< λ_p

3. λ_e> λ_p

4. The relation between λ_e and λ_pdepends on the accelerating potential difference

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. None of these
4. $2.7\dot{A}$

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

2. $\sqrt{2}:1$

3. $2:1$

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

Q.

Assuming the nitrogen molecule is moving with root mean square velocity at $400\mathrm{K}$, the$\mathrm{de}-\mathrm{Broglie}$ wavelength of nitrogen molecule is close to -

(given: nitrogen molecule weight: $4.64\times {10}^{-26}\mathrm{kg}$, Boltzmann constant: $1.38\times {10}^{-23}\mathrm{J}/\mathrm{K}$, Plancks constant: $6.63\times {10}^{-34}\mathrm{Js}$)-

1. $0.44$ $\stackrel{\circ }{\mathrm{A}}$

2. $0.34\stackrel{\circ }{\mathrm{A}}$

3. $0.20\stackrel{\circ }{\mathrm{A}}$

4. $0.24\stackrel{\circ }{\mathrm{A}}$

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

3. $3.3\times {10}^{-34}kgm/s$

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

Q.

A hydrogen atom moving at a speed v absorbs a photon of wavelength 122 nm and stops. Mass of a hydrogen atom = 1.67×${10}^{-27}$ kg. The value of v is .

1. 3.25 m/s
2. 5.48 m/s
3. 6.50 m/s
4. 2.16 m/s.

Q. The electric field of an electromagnetic wave in free space is given by $E=10\cos ({10}^{7}t+kx)\hat{j}V/m$, where $t$ and $x$ are in seconds and metres respectively.
Find the wavelength of the electromagnetic wave.

1. $152.23$ $m$
2. $178.4$ $m$
3. $188.4$ $m$
4. $252.02$ $m$

Q.

A particle is moving $5$ times as fast as an electron. The ratio of the de-Broglie wavelength of the particles to that of the electron is $1.87\times {10}^{-4}.$The mass of the particle is close to:

1. $4.8\times {10}^{-27}\mathrm{kg}$

2. $9.1\times {10}^{-31}\mathrm{kg}$

3. $9.7\times {10}^{-28}\mathrm{kg}$

4. $1.2\times {10}^{-28}\mathrm{kg}$

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. When the momentum of a proton is changed by an amount $P_0$, the corresponding change in the de-Broglie wavelength is found to be $0.25\%$. Then, the original momentum of the proton was

1. $p_0$
2. $100p_0$
3. $400p_0$
4. $4p_0$

Q. When radiation of wavelength $\lambda$ is used to illuminate a metallic surface, the stopping potential is $V$. When the same surface is illuminated with radiation of wavelength$3\lambda$, the stopping potential is $\frac{V}{4}$.If the theshold wavelength for the metallic surface is $n\lambda$ then value of $n$ will be

Q.

An $\alpha$ particle and a proton are accelerated from rest by a potential difference of $200V$. After this, their de Broglie wavelengths are ${\lambda }_{\alpha }$ and ${\lambda }_p$ respectively. The ratio $\frac{{\lambda }_p}{{\lambda }_{\alpha }}$ is:

1. $8$

2. $2.8$

3. $3.8$

4. $7.8$

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. In Lloyd's mirror experiment, a light wave emitted directly by the source $S\left(\text{narrow slit}\right)$ interferes with the wave reflected from a mirror $M$. As a result, an interference fringe pattern is formed on the screen which is $1\text{m}$ far from mirror. The source and the mirror are separated by a distance $l=100\text{cm}$. At a certain position of the source, the fringe width on the screen was equal to $\beta =0.25\text{mm}$ and after the source was moved away from the mirror plane by $\Delta h=0.60\text{mm}$ the fringe width decreased by $1.5\text{times}$. Find the wavelength of light from the source.

1. $0.4\mu \text{m}$
2. $0.2\mu \text{m}$
3. $0.6\mu \text{m}$
4. $1\mu \text{m}$

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.

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 of the matter wave is independent of

1. Mass
2. Momentum
3. Velocity
   
4. Charge

Q. A deuteron and an alpha particle, having equal kinetic energy , enter perpendicular into a magnetic field. Let $r_d$ and $r_{\alpha }$ be their respective radii of circular path. The value of $\frac{r_d}{r_{\alpha }}$ is equal to :

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

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

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. The frequency of the electromagnetic wave, which is best suited to observe a particle of radius $3\times {10}^{-4}cm$ is the order of

1. ${10}^{15}$
2. ${10}^{14}$
3. ${10}^{13}$
4. ${10}^{12}$

Q. 9. The de-Broglie wavelength of 1 MeV proton is(b) 3.33 x 10-30m(d) 2.86 x 10-14m(a) 663 x 10-3Am(c) 2.32 x 10 20m

Q. In photo electric effect, the work function of a metal is $3.5\text{eV}$. The emitted electrons can be stopped by applying a potential of $-1.2\text{V}$. Then -

1. the energy of the incident photon is $4.7\text{eV}$.
2. the energy of the incident photon is $2.3\text{eV}$.
3. if higher frequency photons be used, the photoelectric current will rise.
4. when the energy of photons is $3.5\text{eV}$, the photoelectric current will be maximum.

Q. The electric field in a plane electromagnetic wave is given by
$\overrightarrow{E}=200cos\left[\right(0.5\times {10}^3)x-(1.5\times {10}^{11}\left)t\right]\frac{V}{m}\hat{j}$. This wave falls normally on a perfectly reflecting surface having an area of $100{\text{cm}}^2$. If the radiation pressure exerted by the E.M. wave on the surface during a $10$ minute exposure is $\frac{x}{{10}^9}\frac{N}{m^2}$. Find the value of $x$