Question

A potential of 10000 V is applied across an x-ray tube. Find the ratio of de-Broglie wavelength associated with incident electrons to the minimum wavelength associated with x-rays.
A. `1`
B. `0.1`
C. `0.2`
D. `0.3`

Answer 1

Correct Answer - B
For the incident electron `(1)/(2) mv^(2) = eV` or `p^(2) = 2 meV`
`:.` de - Broglie wavelength `lambda_(1) = (h)/(p) = (h)/(sqrt(2 m eV))`
Shortest `X` - ray wavelength `lambda_(2) = (hc)/(e V)`
`:. (lambda_(1))/(lambda_(2)) = (1)/( c) sqrt(((V)/(2)) ((e )/(m)))= sqrt (10^(2)/(2) xx 1.8 xx 10^(11))/(3 xx 10^(8)) = 0.1`