IIT JEE , AIEEE Forum - Chemistry , Physical Chemistry

khadi_vakeel

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hat velocity should a proton have to have same debroglie wavelength of an electon if the velocity of an electron is v

titun

By the problem,

wavelength = h / (mass of proton x vel. of proton )

= h / ( mass of electron x vel. of electron )

i.e velocity of proton = v x (mass of electron) / (mass of proton) = v / 1836

( since mass of a proton is approx. 1836 times heavier than an electron)

Ans: v /1836

edison

De broglie wavelength of a particle is given by

= h/p

where

= debroglie wavelength

p = mv = momentum of the given particle.

Now mass of electron = m_e

velocity of electron = v

corresponding to which wavelength of electron is =

_e= h/ m_ev

let proton velocity = v'

mass of proton = 1836 m_e

so proton wavelength =

_p= h /1836m_ev'

for

_e=

_p

or h/ m_ev = h /1836m_ev'

or v' = v/1836

is the required velocity of proton.