Two particles A and B are in motion. If the wavelength associated with the particle 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

`lambda_A = 33.33 nm = 33.33 xx 10^(-9)m`
`p_B = 1/3 p_A`
`lambda_A = h/(p_A)`
`lambda_A = h/(p_A) " " ….(i)`
`lambda_B = h/(rho_B) = h/(p_A//3) = (3h)/(p_A) " " …..(ii)`
From eq. (i) and (ii)
`(lambda_A)/(lambda_B) = 1/3`
`:. lambda_B = 3 xx lambda_A = 3 xx 33.33 xx 10^(-9) m`
`= 1.0 xx 10^(-7) m` .