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.

Answer 1

Explanation:

In the question, it is given:

Electron energy in the K shell, $E_{\mathrm{k}}=25.31 \mathrm{keV}$

Electron energy in the M shell, $E_{M}=0.530 \mathrm{keV}$

Electron energy in the L shell, $E_{L}=3.56 \mathrm{keV}$

Let the K’s frequency be f.

f0 and αX-ray be the Kβ X-ray’s frequency.

Let the Lα X-rays of silver’s frequency be f1.

Therefore, $\mathrm{K}_{a}=h f=E_{\mathrm{K}}-E_{\mathrm{L}}$

Here, h = Constant of Planck  

f = K’s frequency,

αX-ray

$\mathrm{f}=\mathrm{EK}-\mathrm{E} \ln \mathrm{f}=(25.31-3.56) 6.63 \times 10-34 \times 1.6 \times 10-9 \times 103 \mathrm{f}$

$=5.25 \times 1018 \mathrm{HzK} \beta$

$=\mathrm{EK}-\mathrm{EM}=\mathrm{hfo}$

$\Rightarrow \mathrm{f} 0=(25.31-0.53) 6.67 \times 10-34 \times 103 \times 1.6 \times 10-19$

$\Rightarrow \mathrm{f} 0=7.32 \times 1017 \mathrm{Hz}$