Question

To produce characteristic X-rays using a Tungsten target in an X-rays generator, the accelerating voltage should be greater than _________ volts and the energy of the characteristic radiation is _________ eV. Binding energy of the inner most electron in Tungsten $=40KeV$.

• A. $60000,40000$
• B. $30000,30000$
• C. $40000,30000$
• D. $40000,40000$

Answer 1

The correct option is B $30000,30000$

Electron shall jump from $h=2$ to $n=1$

For characteristic $x-$ray

$\frac{1}{\lambda }=R_{\alpha }(2-1{)}^2[1-\frac{1}{n^2}]=\frac{E}{nC}$

$\therefore \frac{E_1}{nC}=R_{\alpha }(2-1{)}^2[1-\frac{1}{2^2}]$ ... (i)

Binding energy = $40KeV$

$\therefore$ Ionization potential of tungsten = $40\times {10}^3\times$

$\frac{E_1}{E_2}=\frac{[1-\frac{1}{2^2}]}{[1-\frac{1}{{\infty }^2}]}$ $\therefore E_1=\frac{3}{4}\times 40,000$

$E_1=30,000eV$

$V_{min}=\frac{E_1}{e}=30,000V$