If `E_1 ,E_2 and E_3` represent, respectively, the kinetic energies of an electron, an alpha partile and proton , each having the same de Broglie wavelength, then

Options

A. `E_1 gt E_3 gt E_2`
B. `E_2 gt E_3 gt E_1`
C. `E_1 gt E_2 gt E_3`
D. `E_1 = E_2 = E_3`

Answer

A

Explanation

Since, `KE =1/2 mv^2 and lambda=h/(mv)`
`:. KE = 1/2 m (h^2)/(m^2 lambda^2) = h^2/(2m lambda^2)`
As, `lambda` is the same,
`:. KE prop 1/m`