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

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

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Initial momentum is 200pm

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 pm