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

Answer

C

Explanation

de-Broglie wavelength `lamda=h/(mv)`
where, mv= p (moment)
`implies" "lamda= h/pimpliesp=h/(lamda)`
Here, h is a constant.
So, `" "p prop1/(lamda)implies(p_(1))/(p_(2))=(lamda_(2))/(lamda_(1))`
`But " "(lamda_(1)=lamda_(2))=lamda`
`Then, " "p_(1)/p_(2)=(lamda)/(lamda)=1impliesp_(1)=p_(2)`
Thus, their momenta is same.
`Also, " "E=1/2mv^(2)=1/2(mv^(2)xxm)/(m)`
`" "=1/2(m^(2)v^(2))/(m)=1/2(p^(2))/(m)`
Here, p is constant `" "E prop1/m`
`therefore" "(E_(1))/(E_(2))=(m_(2))/(m_(1))lt1impliesE_(1)ltE_(2)`