A metal target with atomic number Z = 46 is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio of the wavelengths of the -line and the cut-off is found to be . If the same electron beam bombards anot

Question

A metal target with atomic number Z = 46 is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio $r$ of the wavelengths of the $K_{α}$ -line and the cut-off is found to be $r = 2$ . If the same electron beam bombards another metal target with Z = 41, the value of $r$ will be [2024]

Smart Achievers · Accepted Answer

(1)

The ratio of the wavelengths of the $K_{α}$ -line and the cut-off i.e.

$\frac{λ_{K_{α}}}{λ_{0}} (= r) \propto \frac{1}{{(Z - 1)}^{2}}$

$∴$ $\frac{r_{2}}{r_{1}} = \frac{{(Z_{1} - 1)}^{2}}{{(Z_{2} - 1)}^{2}} = \frac{{(46 - 1)}^{2}}{{(41 - 1)}^{2}} = \frac{45^{2}}{40^{2}}$

or, $r_{2} = 1.265 \times r_{1} = 1.265 \times 2 = 2.53$

Solution

1 2.53

2 1.27

3 2.24

4 1.58

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