The de-Broglie wavelength is proportional to 
(1) $\mathrm{\lambda }\propto \frac{1}{\mathrm{v}}$               

(2) $\mathrm{\lambda }\propto \frac{1}{m}$

(3) $\mathrm{\lambda }\propto \frac{1}{p}$               

(4) $\mathrm{\lambda }\propto \mathrm{p}$

Particle nature and wave nature of electromagnetic waves and electrons can be shown by 

(1) Electron has small mass, deflected by the metal sheet

(2) X-ray is diffracted, reflected by thick metal sheet

(3) Light is refracted and defracted

(4) Photoelectricity and electron microscopy

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

(a) $7.25\times {10}^6$ m/s                   (b) $6.26\times {10}^6$ m/s 
(c) $5.25\times {10}^6$ m/s                   (d) $4.24\times {10}^6$ m/s

The kinetic energy of electron and proton is ${10}^{-32}$ J. Then the relation between their de-Broglie wavelengths is

(1) ${\mathrm{\lambda }}_{\mathrm{p}}<{\mathrm{\lambda }}_{\mathrm{e}}$                 

(2) ${\mathrm{\lambda }}_{\mathrm{p}}>{\mathrm{\lambda }}_{\mathrm{e}}$

(3) ${\mathrm{\lambda }}_{\mathrm{p}}={\mathrm{\lambda }}_{\mathrm{e}}$                 

(4) ${\mathrm{\lambda }}_{\mathrm{p}}=2{\mathrm{\lambda }}_{\mathrm{e}}$

The de-Broglie wavelength of a particle accelerated with 150 volt potential is ${10}^{-10}$ m. If it is accelerated by 600 volts p.d., its wavelength will be
(1) 0.25 Å                 

(2) 0.5 Å

(3) 1.5 Å                   

(4) 2 Å

The de-Broglie wavelength associated with a hydrogen molecule moving with a thermal velocity of 3 km/s will be
(1) 1 Å                     

(2) 0.66 Å

(3) 6.6 Å                 

(4) 66 Å

When the momentum of a proton is changed by an amount ${\mathrm{P}}_0$, the corresponding change in the de-Broglie wavelength is found to be 0.25%. Then, the original momentum of the proton was 
(a) ${\mathrm{P}}_0$                   (b) 100  ${\mathrm{P}}_0$
(c) 400 ${\mathrm{P}}_0$             (d) 4 ${\mathrm{P}}_0$

The de-Broglie wavelength of a neutron at 27 $°\mathrm{C}$ is $\mathrm{\lambda }$. What will be its wavelength at 927 $°\mathrm{C}$
(a) $\mathrm{\lambda }$ / 2                        (b) $\mathrm{\lambda }$ / 3
(c) $\mathrm{\lambda }$ / 4                        (d) $\mathrm{\lambda }$ / 9