Two particles `A_(1) and A_(2)` of masses `m_(1), m_(2) (m_(1)gtm_(2))` have the same de-broglie wavelength. Then

Options

A. their momenta are the same.
B. their energies are the same.
C. momentum of `A_(1)` is less than the momentum of `A_(2)`.
D. energy of `A_(1)` is more than the energy of `A_(2)`.

Answer

A

Explanation

(a) : As `lamda=(h)/(p) or p=(h)/(lamda) or pprop(1)/(lamda)`
`:.(p_(1))/(p_(2))=(lamda_(2))/(lamda_(1))=(lamda)/(lamda)=1 or p_(1)=p_(2)`
Also `E=(1)/(2)(p^(2))/(m)=(1)/(2m)(h^(2))/(lamda^(2))" "(becausep=(h)/(lamda))`
or ` Eprop(1)/(m):.(E_(1))/(E_(2))lt1 or E_(1)ltE_(2)`