An electron $\left(mass<mspace\; width="1em"></mspace>m\right)$ with an initial velocity v=${\mathrm{v}}_0\hat{\mathrm{i}}<mspace\; width="1em"></mspace>\left({\mathrm{v}}_0>0\right)$ is in an electric field E$=-E_0<mspace\; width="1em"></mspace>\hat{i}\left(E_0=cons\tan t<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>0\right).$ It's de Broglie wavelength at the time $t$ is given by:

1. $\frac{{\lambda }_0}{\left(1+{\displaystyle \frac{e{E}_0}{m}}{\displaystyle \frac{t}{v_0}}\right)}$

2. ${\lambda }_0\left(1+\frac{e{E}_{0}t}{m{v}_0}\right)$

3. ${\lambda }_0$

4. ${\lambda }_{0}t.$

The ratio of momenta of an electron and an $\mathrm{}$\(\alpha \text-\)particle which are accelerated from rest by a potential difference of \(100~\text{V}\) is:
1. \(1\)
2. \(\sqrt{\frac{2m_e}{m_{\alpha}}}\)
3. \(\sqrt{\frac{m_e}{m_{\alpha}}}\)
4. \(\sqrt{\frac{m_e}{2m_{\alpha}}}\)

The fact that electric charges are integral multiples of the fundamental electronic charge was proved experimentally by 
(1) Planck                   

(2) J.J. Thomson

(3) Einstein                 

(4) Millikan

 A narrow electron beam passes undeviated through an electric field E = $3\times {10}^4<mspace\; width="1em"></mspace>\mathrm{volt}/\mathrm{m}$ and an overlapping magnetic field $\mathrm{B}=2\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{Weber}/{\mathrm{m}}^2$. If electric field and magnetic field are mutually perpendicular. The speed of the electrons is 
1. \(60\) m/s                       
2. $10.3\times {10}^7<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$
3. $1.5\times {10}^7<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$             
4. $0.67\times {10}^{-7<mspace\; width="1em"></mspace>}\mathrm{m}/\mathrm{s}$

The specific charge of an electron is 

(a) $1.6\times {10}^{-19}$ coulomb

(b) $4.8\times {10}^{-10}$ stat coulomb

(c) $1.76\times {10}^{11}$ coulomb/kg

(d) $1.76\times {10}^{-11}$  coulomb/kg

Cathode rays are similar to visible light rays in that

(1) They both can be deflected by electric and magnetic fields

(2) They both have a definite magnitude of wavelength

(3) They both can ionize a gas through which they pass

(4) They both can expose a photographic plate

A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20<mspace\; width="1em"></mspace>{\mathrm{Vm}}^{-1}$ and 0.5 T at right angles to the direction of motion of the electrons. What is the velocity of the electrons

1. 20 ${\mathrm{ms}}^{-1}$                  2. 40 ${\mathrm{ms}}^{-1}$ 
3. 8 ${\mathrm{ms}}^{-1}$                    4. 5.5 ${\mathrm{ms}}^{-1}$

Electron volt is a unit of 
(1) Potential                         

(2) Charge

(3) Power                             

(4) Energy

The ratio of specific charge of an $\mathrm{\alpha }$-particle to that of a proton is 
(1) 2 : 1                     

(2) 1 : 1

(3) 1 : 2                     

(4) 1 : 3

In Bainbridge mass spectrograph a potential difference of 1000 V is applied between two plates distant 1 cm apart and magnetic field in B = 1T. The velocity of undeflected positive ions in m/s from the velocity selector is

(1)${10}^7<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$                    

(2) ${10}^4<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$

(3) ${10}^5<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$                   

(4) ${10}^2<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$