A moving particle is associated with wavelength `5xx10^(-8) m`. If its momentum is reduced to half of its value compute the new wavelength. If answer is `10^(-x)` then find 'x'.

Answer

7

Explanation

Given `lambda=5xx10^(8) m`
`lambda=h/(mv)=(h)/("momentum")`
`:. Lambda_(1)/lambda_(2)=(("momentum")_(2))/(("momentum")_(1))`
Since, `(momentum)_(2)=1/2 ("momentum")_(1)`
Or `lambda_(2)=(("momentum")_(1)xxlambda_(1))/(("momentum")_(2))=2xx5xx10^(-8)=10^(-7) m`