The ratio of the de-Broglie wavelengths of an electron of energy 10 eV to that of a person of mass 66kg traveling 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

For an electron
Mass , `m_e = 9.11 xx 10^(-31) kg `
Kinetic energy , `K= 10 eV = 10 xx 1.6 xx 10^(-19)J`
de Broglie wavelength `lamda_(e) = h/(sqrt(2m_(e) K)) " "...(i)`
For the person
Mass, m = 66 kg ,
Speed , `v = 100 km h^(-1) = 100 xx 5/(18) ms^(-1)`
de Broglie wavelength `lamda= h/(mv) " "...(ii)`
Divide (i) by (ii) , we get
`(lamda_e)/lamda=h/(sqrt(2m_eK)) xx(mv)/h`
`=(mv) / (sqrt(2m_eK) ) =(6.6 xx 100 xx 5/18)/(sqrt(2xx9.11 xx 10^(-31) xx10 xx 1.6 xx 10^(-19))) = 1.07 xx 10^(27)`