If an X-ray tube operates at the voltage of 10kV, find the ratio of the de-broglie wavelength of the incident electrons to the shortest wavelength of X-ray producted. The specific charge of electron is `1.8xx10^11 C/(kg)`.

Options

A. `0.1`
B. `0.2`
C. `0.3`
D. `1.0`

Answer

A

Explanation

For incident electron ,`(1)/(2)mv^(2)=eV`
or `" " p^(2)=2meV`
`:.` de-Broglie wavelength , `lambda_(1)=(h)/(p)=(h)/(sqrt(2mev))`
Shortest X-rays wavelength, `lambda_(2)=(hc)/(eV)`
`:. " " (lamda_(1))/(lambda_(2))=(1)/(c)sqrt(((V)/(2))((e)/(m)))`
`" " =sqrt((10^(4))/(2)xx1.8xx10^(11))/(3xx10^(8))=0.1`