Two particles A and B are in motion. If the wavelength associated with the particle A is `5 xx 10^(-8) m` , calculate the wavelength of particle B, if its momentum is half of A.

Explanation

According to de-Broglie relation,
`lamda = h/p " or " p = h/lamda `
for particle A , `p_A= (h)/(lamda_A)`
Here, `p_A` and `lamda_A` are the momentum and wavelength of particle A.
for particle B `p_B = (h)/(lamda_B)`
Here` p_B` and `lamda_B` are the momentum and wavelength of particle B.
But `p_B = 1/2 p_A`
` therefore (h)/(lamda_B) = 1/2 (h)/(lamda_A)`
`(lamda_A)/(lamda_B) = 1/2 ` or `lamda_B = 2lamda_A`
But `lamda_A = 5 xx 10^(-8) m`
`lamda_B = 2lamda_A = 2 xx 5 xx 10^(-8) m = 10 xx 10^(-8) m = 10^(-7) m`