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

(1) $\sqrt{2}:1$              

(2) 2:1

(3) $2\sqrt{2}:1$             

(4) $\frac{1}{2\sqrt{2}}:1$

The wavelength of de-Broglie wave is 2$\mathrm{\mu }$m, then its momentum is (h = $6.63\times {10}^{-34}$ J-s) 
(a) $3.315\times {10}^{-28}$ kg-m/s            (b) $1.66\times {10}^{-28}$ kg-m/s
(c) $4.97\times {10}^{-28}$ kg-m/s              (d) $9.9\times {10}^{-28}$ kg-m/s

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

The energy that should be added to an electron to reduce its de Broglie wavelength from one nm to 0.5 nm is

(a) Four times the initial energy

(b) Equal to the initial energy

(c) Twice the initial energy

(d) Thrice the initial energy

The wavelength of the matter wave is independent of

(1) Mass                 

(2) Velocity

(3) Momentum       

(4) Charge

Kinetic energy with which the electrons are emitted from the metal surface due to photoelectric effect is 

(1) Independent of the intensity of illumination

(2) Independent of the frequency of light

(3) Inversely proportional to the intensity of illumination

(4) Directly proportional to the intensity of illumination

The number of photo-electrons emitted per second from a metal surface increases when

(1) The energy of incident photons increases

(2) The frequency of incident light increases

(3) The wavelength of the incident light increases

(4) The intensity of the incident light increases

The work function for tungsten and sodium are 4.5 eV and 2.3 eV respectively. If the threshold wavelength $\mathrm{\lambda }$ for sodium is 5460 Å, the value of $\mathrm{\lambda }$ for tungsten is

(1) 5893 Å                   

(2) 10683 Å

(3) 2791 Å                   

(4) 528 Å

Light of wavelength 4000 Å is incident on a sodium surface for which the threshold wave length of photo – electrons is 5420 Å. The work function of sodium is

(1) 4.58 eV                 

(2) 2.29 eV

(3) 1.14 eV                 

(4) 0.57 eV

Stopping potential for photoelectrons 

(1) Does not depend on the frequency of the incident light

(2) Does not depend upon the nature of the cathode material

(3) Depends on both the frequency of the incident light and nature of the cathode material

(4) Depends upon the intensity of the incident light