Question

When two different material A and B having atomic number $z_1$ and $z_2$ are used as the target in Coolidge $\gamma$- ray tube at different operating voltage $V_1$ and $V_2$ respectively their sprectrums are found as below. The correct relation is

• A. $V_1$ > $V_2,z_1$ > $z_2$
• B. $V_1$ < $V_2,z_1$ < $z_2$
• C. $V_1$ < $V_2,z_1$ > $z_2$
• D. $V_1$ > $V_2,z_1$ < $z_2$

Answer 1

The correct option is A $V_1$ > $V_2,z_1$ > $z_2$

Here ${\lambda }_{min}=\frac{hc}{eV}\Rightarrow \lambda \propto \frac{1}{v}Since{\lambda }_2$ > ${\lambda }_2$
$\Rightarrow V_1$ > $V_2$
We know that, $\sqrt{f}$ = a(z-b) mosley’s law
$\Rightarrow \frac{1}{\lambda }\propto (z-1{)}^2\Rightarrow \lambda \propto \frac{1}{(z-1{)}^2}\therefore since{\lambda }_2$ > ${\lambda }_1$
$\Rightarrow z_1$ > $z_2$ ....(2)