SATHEE: Modern Physics 4 Question 10

Modern Physics 4 Question 10

10. If $λ_{C u}$ is the wavelength of $K_{α}, X$ -ray line of copper (atomic number 29) and $λ_{M O}$ is the wavelength of the $K_{α}$ , X-ray line of molybdenum (atomic number 42 ), then the ratio $λ_{C u} / λ_{M o}$ is close to

(2014 Adv.)

(a) 1.99

(b) 2.14

(d) 0.48

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Solution:

$K_{α}$ transition takes place from $n_{1} = 2$ to $n_{2} = 1$

$∴ \frac{1}{λ} = R (Z - b)^{2} \frac{1}{(1)^{2}} - \frac{1}{(2)^{2}}$

For $K$ -series, $b = 1$

$\begin{aligned} ∴ & \frac{1}{λ} \propto (Z - 1)^{2} \\ \Rightarrow \frac{λ_{C u}}{λ_{M o}} & = \frac{{(z_{M o} - 1)}^{2}}{{(z_{C u} - 1)}^{2}} = \frac{(42 - 1)^{2}}{(29 - 1)^{2}} \\ = \frac{41 \times 41}{28 \times 28} = \frac{1681}{784} = 2.144 \end{aligned}$

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Modern Physics 4 Question 10

10. If λCu is the wavelength of Kα,X-ray line of copper (atomic number 29) and λMO is the wavelength of the Kα, X-ray line of molybdenum (atomic number 42 ), then the ratio λCu/λMo is close to

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10. If $λ_{C u}$ is the wavelength of $K_{α}, X$ -ray line of copper (atomic number 29) and $λ_{M O}$ is the wavelength of the $K_{α}$ , X-ray line of molybdenum (atomic number 42 ), then the ratio $λ_{C u} / λ_{M o}$ is close to