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

Explanation

According to de-Broglie equation,
`lambda = h/p`
For particle A : `lambda_A = h/(p_A)" "….(i) `
For particle B : `lambda_B = h/(p_B) " " …..(ii) `
But `p_B = (p_A)/(2)`
`:. lambda_B = h/(p_B) = h/(p_A//2) = (2h)/(p_A) " ".....(iii)`
From equation (i) and (iii),
`(lambda_A)/(lambda_B) = 1/2 "or" lambda_B = 2 lambda_A`
Now, `lambda_A = 5 xx 10^(-8) m`
`:. lambda_B = 2 xx 5 xx 10^(-8) = 10^(-7) m`.