Question

In the diagram, a graph between the intensity of $X$ -rays emitted by a molybdenum target and the wavelength is shown. The graph is obtained for electrons of $30keV$ incident on the target. In the graph, one peak is of $K_{\alpha }$ line and the other peak is of $K_{\beta }$ line. Which of the following statements must be true?

• A. The first peak is of $K_{\alpha }$ line at $0.6$ $\stackrel{{}^{\circ }}{A}$ .
• B. The highest peak is of $K_{\alpha }$ line at $0.7\stackrel{{}^{\circ }}{A}$ .
• C. If the energy of incident particles is increased, then the peaks will shift towards left.
• D. If the energy of incident particles is increased, then the peaks will shift towards right.

Answer 1

Answer: (B)

$\Delta E=\frac{hc}{\lambda }...\left(1\right)$
$K_{\alpha }$ is the production of $X$ -ray by transition from, $n=2$ to $n=1$ .
$K_{\beta }$ is the production of $X$ -ray by transition from, $n=3$ to $n=1$ .
As, $E_{K_{\beta }}>E_{K_{\alpha }}$ , from $\left(1\right)$ , we get,
${\lambda }_{K_{\alpha }}>{\lambda }_{K_{\beta }}$ .
So, $\lambda =0.7A$ for $K_{\alpha }$ .