Question

A cobalt target $($atomic no $=27)$ is bombarded with electrons and the wavelength of its characteristic $X-$ray spectrum are measured. A second weak characteristic spectrum is also found, due to presence of an impurity in the target. The wavelengths of the $K_{\alpha }$ lines are $225\text{pm}$ for cobalt and $100\text{pm}$ for impurity. If the atomic number of impurity is $5N$, find the value of $N$.

• A. $10$
• B. $40$
• C. $5$
• D. $8$

Answer 1

The correct option is D $8$

We know that Moseley's law,

$\sqrt{f}=a(Z-b)$

For $K_{\alpha }$ lines, $b=1$

So, $\sqrt{f}=a(Z-1)$

$\Rightarrow \sqrt{\frac{c}{\lambda }}=a(Z-1)$

$\Rightarrow \frac{{\lambda }_{\text{co}}}{{\lambda }_{\text{im}}}={\left(\frac{Z_{\text{im}}-1}{Z_{\text{co}}-1}\right)}^2$

$\Rightarrow \frac{225}{100}={\left(\frac{Z_{\text{im}}-1}{27-1}\right)}^2$

On solving this, we get,

$Z_{\text{im}}=40=5N$

$\therefore N=8$

Why this question? Tip: The frequency of emitted $X-$ray can be given as $f=c/\lambda$ as it is an electromagnetic wave.

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