The ratio of the de-Broglie wavelengths of an electron of energy 10 eV to that of a person of mass 66kg travelling with a speed of `100km//h` is of the order of

Options

A. `10^(34)`
B. `10^(27)`
C. `10^(17)`
D. `10^(-10`

Answer

b

Explanation

Here, for the electron, `m_(e)=9.1xx10^(-31) kg`,
`K=10 eV=10xx1.6xx10^(-19)J`
De-Broglie wavelength, `lambda_(e)=h/(sqrt(2m_(e)K))........(i)`
For the persons, `m=66kg`,
`v=100km//h=100xx5/18m//s`
De-broglie wavelength, `lambda=h/(mv)........(ii)`
`:. (lambda_(e))/lambda=(mv)/(sqrt(2m_(e)K))`
`=(66xx100xx(5//18))/(sqrt(2xx9.1xx10^(-31)xx10xx1.6xx10^(-19)))`
`=1.07xx10^(27)`