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.

Options

A. `1:10`
B. `10:1`
C. `5:1`
D. `1:5`

Answer

A

Explanation

For the incident electron,
`(1)/(2) m v^(2) = ve`
`p^(2) = 2 meV`
de Broglie wavelength of incident electron,
`lambda_(1) = (h)/(p) = (h)/sqrt(2 m Ve)`
Shortest X-ray wavelength , `lambda_(2) = (h c)/(Ve)`
`:. (lambda_(1))/(lambda_(2)) = (Ve)/(e sqrt(2 m Ve))`
`= (1)/(e) sqrt(((V)/(2)) (e)/(m)) = (sqrt((10^(4))/(2) xx 1.8 xx 10^(11)))/(3 xx10^(8)) = 0.1 = (1)/(10)`
or `lambda_(1) : lambda_(2) = 1:10`