Question

A graph of $\sqrt{v}$ (where $v$ is the frequency of $K_{\alpha }$ line of the characteristic $X$-ray spectrum ) is plotted against the atomic number $Z$ of the elements emitting the characteristic $X$-ray .The intercept of the graph on the $z$-axis is $1$ and the slope of the graph is $0.5\times 10^8$ in $SI$ units. The frequency of the $K_{\alpha }$ line for an element of atomic number $41$ is given as $\alpha \times 10^{16}Hz$. Find the value of $\alpha$.

Answer 1

Answer: 400

From the given information,
$\sqrt{v}=m[Z-1]$
$\Rightarrow \sqrt{v}=5\times 10^7(Z-1)$
For $Z=41,v={\left[5\times 10^7\times (40)\right]}^2$
$=400\times 10^{16}Hz$