Kα wavelength emitted by an atom of atomic number Z=11 is λ . Find the atomic number for an atom that emits Kα radiation with wavelength 4λ .

Question

Kα wavelength emitted by an atom of atomic number Z=11 is λ . Find the atomic number for an atom that emits Kα radiation with wavelength 4λ . (A) Z=6 (B) Z=4 (C) Z=11 (D) Z=44

Tardigrade Admin · Accepted Answer

(1/λ) propto( Z -1)2 ∴ (λ1/λ2)=(( z 2-1)2/( z1-1)2) (1/4)=(( Z 2-1/11-1))2 Solving this, we get, Z2=6

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 $4 λ$ .

$Z = 6$

$Z = 4$

$Z = 11$

$Z = 44$

$\frac{1}{λ} \propto (Z - 1)^{2}$
$∴ \frac{λ _{1}}{λ _{2}} = \frac{( z _{2} - 1 ) ^{2}}{( z _{1} - 1 ) ^{2}}$
$\frac{1}{4} = (\frac{Z _{2} - 1}{11 - 1})^{2}$
Solving this, we get, $Z_{2} = 6$

Q. Kα​ wavelength emitted by an atom of atomic number Z=11 is λ . Find the atomic number for an atom that emits Kα​ radiation with wavelength 4λ .

Z=6

Z=4

Z=11

Z=44