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Question
The energy of a silver atom with a vacancy in K shell is 25.31 keV, in L shell is 3.56 keV and in M shell is 0.530 keV higher than the energy of the atom with no vacancy. Find the frequency of Kα, Kβ and Lα X-rays of silver.
(Use Planck constant h = 6.63 × 10-34 Js= 4.14 × 10-15 eVs, speed of light c = 3 × 108 m/s.)
Solution
Given:-
Energy of electron in the K shell, Ek = 25.31 keV
Energy of electron in the L shell, EL = 3.56 keV
Energy of electron in the M shell, EM = 0.530 keV
Let f be the frequency of Kα X-ray and f0 be the frequency of Kβ X-ray.
Let f1 be the frequency of Lα X-rays of silver.
∴ Kα = EK − EL = hf
Here, h = Planck constant
f = frequency of `Kα` X-ray
`f = (E_K - E_L)/h`
`f = ((25.31 xx 3.56))/(6.63 xx 10^-34) xx 1.6 xx 10^-19 xx 10^3`
`f = (21.75 xx 10^3 xx 10^15)/6.67`
`f = 5.25 xx 10^18 "Hz"`
`K_β = E_K - E_M = hf_0`
`⇒ f_0 = (E_K - E_M)/h`
`⇒ f_0 = ((25.31 - 0.53))/(6.67 xx 10^-34) xx 10^3 xx 1.6 xx 10^-19`
`⇒ f_0 = 5.985 xx 10^18 "Hz"`
`K_L = E_L - E_M = hf_1`
`f_1 = (E_L - E_M)/h`
`f_1 = (3.56 - 0.530)/(6.63 xx 10^-34) xx 10^3 xx 1.6 xx 10^-19`
`f_1 = 7.32 xx 10^17 "Hz"`
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