wavelength emitted by an atom of atomic number Z = 11 is . Find the atomic number for an atom that emits radiation with wavelength . [2005]

Question

$K_{α}$ wavelength emitted by an atom of atomic number Z = 11 is $λ$ . Find the atomic number for an atom that emits $K_{α}$ radiation with wavelength $4 λ$ . [2005]

Smart Achievers · Accepted Answer

(1)

$For K_{α}, \frac{1}{λ} \propto {(Z - 1)}^{2}$

$∴$ $\frac{λ_{2}}{λ_{1}} = \frac{{(Z_{1} - 1)}^{2}}{{(Z_{2} - 1)}^{2}}$ $\Rightarrow \frac{4 λ}{λ} = \frac{{(11 - 1)}^{2}}{{(Z_{2} - 1)}^{2}}$

$\Rightarrow Z_{2} - 1 = \frac{10}{2}$

$∴$ $Z_{2} = 6$

Solution

Q.
$K_{α}$ wavelength emitted by an atom of atomic number Z = 11 is $λ$ . Find the atomic number for an atom that emits $K_{α}$ radiation with wavelength $4 λ$ . [2005]

1 Z = 6

2 Z = 4

3 Z = 11

4 Z = 44

Ans.
(1)

$For K_{α}, \frac{1}{λ} \propto {(Z - 1)}^{2}$

$∴$ $\frac{λ_{2}}{λ_{1}} = \frac{{(Z_{1} - 1)}^{2}}{{(Z_{2} - 1)}^{2}}$ $\Rightarrow \frac{4 λ}{λ} = \frac{{(11 - 1)}^{2}}{{(Z_{2} - 1)}^{2}}$

$\Rightarrow Z_{2} - 1 = \frac{10}{2}$

$∴$ $Z_{2} = 6$

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