Find the (a) maximum frequency and (b) minimum wave-length of X-rays produced by 30 kV electrons. Given, `h=6.63xx10^(-34)Js`.

Explanation

Potential of the electrons , V=30 kV = `3xx10^(4)` V
Hence, energy of the electrons , E`=3xx10^4` eV
Where, e = charge on an electron `=1.6xx10^(-19)C`
(a)Maximum frequency produced by the X-rays =v The energy of the electrons is given by the relation :
E=hv
Where,
h=Planck's constant =`6.626xx10^(-34) Js`
`therefore v=E/h`
`=(1.6xx10^(-19)xx3xx10^(4))/(6.626xx10^(-34))=7.24xx10^(18)` Hz
Hence , the maximum frequency of X-rays produced is `7.24xx10^(18)`Hz
(b)The minimum wavelength produced by the X-rays is given as :
`lambda=c/v`
`=(3xx10^8)/(7.24xx10^(18))=4.14xx10^(-11) m =0.0414 nm`
Hence , the minimum wavelength of X-rays produced is 0.0414 nm