Question

Find the initial momentum of electron if the momentum of electron is changed by P_m and the De Broglie wavelength associated with it changes by 0.50 %

Answer 1

Initial momentum is 200p_m 

Explaination:

\({d\lambda\over\lambda}\times 100 =0.5 \)

\({d\lambda\over\lambda}\times 100 ={0.5\over100}={1\over200}\)  and \(\triangle p=p_m\) 

\(p={h\over\lambda},\) differentiating

 \({dp\over d\lambda}=-{h\over \lambda^2}={-h\over \lambda}\times{1\over\lambda}={-p\over \lambda}\) 

\({|dp|\over p}={d\lambda\over \lambda} \therefore {p_m\over p}={1\over 200}\) 

p=200 p_m