Two particle A and B are in motion. If the wavelength associated with 'A' is 33.33 nm, the wavelength associated with 'B' whose momentum is `1//3^(rd)` of 'A' is

Options

A. `1.0 xx 10^(-8)` m
B. `2.5 xx 10^(-8)` m
C. `1.25 xx 10^(-7)` m
D. `1.0 xx 10^(-7)` m

Answer

D

Explanation

(d): `lamda_(A) =33.3` nm = `33.33 xx 10^(-9)` m
`lamda_(A) = h//p_(A)` ...(i)
`lamda_(B) = (h)/(p_(A)//3) = (3h)/(p_(A))` ...(ii)
From eq (i) and (ii), we get
`(lamda_(A))/(lamda_(B)) = 1/3 rArr lamda_(B) = 33.33 xx 10^(-9) xx 3 =99.99 xx 10^(-9)` m
`~~ 1.0xx10^(-7)` m