The de-Broglie wavelength ` lambda` associated with a proton increases by ` 25%` . If its momentum is decreased by ` p_(0)` , find its initial momentum .

Explanation

Suppose increased wavelength is `lambda.`
Then , `lambda. = lambda + 25% " of " lambda = (5 lambda)`
Now, momentum ` rho (h)/( lambda)`
`:. rho - rho_(0) = (h)/( lambda.) = (h)/( 5 lambda // 4) = (4h)/( 5 lambda)`
`rArr rho = rho_(0)+ (4h)/( 5 lambda) = rho_(0) + (4)/(5) rho`
`rArr rho_(0) =rho - (4)/(5) rho = (1)/(5) rho`