A particle of mass \(1\) mg has the same wavelength as an electron moving with a velocity of \(3\times 10^{6}~\text{m/s}\). What will be the velocity of the particle? (mass of electrons = \(9.1\times 10^{-31}\) kg)

1.	\(2.7 \times 10^{-18} ~\text{ms}^{-1}\)
2.	\(9 \times 10^{-2} ~\text{ms}^{-1}\)
3.	\(3 \times 10^{-31}~\text{ms}^{-1}\)
4.	\(2.7 \times 10^{-21} ~\text{ms}^{-1}\)

An electron $\left(mass m\right)$ with an initial velocity v=${\mathrm{v}}_0\hat{\mathrm{i}} \left({\mathrm{v}}_0>0\right)$ is in an electric field E$=-E_0 \hat{i}\left(E_0=cons\tan t > 0\right).$ 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)${\lambda }_{0}t.$

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

Electron volt is a unit of 
(1) Potential                         

(2) Charge

(3) Power                             

(4) Energy

In an electron gun, the electrons are accelerated by the potential V. If e is the charge and m is the mass of an electron, then the maximum velocity of these electrons will be

(1) $\frac{2\mathrm{eV}}{\mathrm{m}}$                   

(2) $\sqrt{\frac{2\mathrm{eV}}{\mathrm{m}}}$

(3) $\sqrt{\frac{2\mathrm{m}}{\mathrm{eV}}}$                 

(4) $\frac{{\mathrm{V}}^2}{2\mathrm{em}}$

The idea of matter waves was given by
(1) Davisson and Germer                 

(2) de-Broglie

(3) Einstein                                     

(4) Planck

Waves are associated with matter only:

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

A photon, an electron, and a uranium nucleus all have the same wavelength. The one with the most energy: 

(1) Is the photon

(2) Is the electron

(3) Is the uranium nucleus

(4) Depends upon the wavelength and the properties of the particle