Calculate the de Broglie wavelength of a proton whose kinetic energy is equal to `81.9 xx 10^(-15) J`. (Given `:` mass of proton is 1836 times that of electron ) .

Explanation

Kinetic energy of the proton `E_(k) =81.9 xx 10^(-15) J`
Mass of the proton `m_(p) = 1836 m_(e ). [m_(e ) = 9.1 xx 10^(-31) ]`
To find `:`
`lambda = ( h )/(mv ) ` ( or ) ` ( h ) /(sqrt( 2m E _(k)))`
`= ( 6.6 xx 10^(-34))/( sqrt( 2 xx 1836 xx 9.1 xx 10^(-31) xx 81.9 xx 10^(-15)))`
`= ( 6.6 xx 10^(-34))/( sqrt( 2736705 xx 10^(-46))) = ( 6.6 xx 10^(-34))/( 1.64 xx 10^(-20))`
`lambda = 4.02 xx 10^(-14) m `