Question

The wavelengths of the Kα X-ray radiations from two sources P and Q are 1.50 ˚A and 0.75 ˚A (1 ˚A= 10−10m). Then most likely,

Answer 1

Wa complete question is ------> The wavelengths of the Kα X-ray radiations from two sources P and Q are 1.50 ˚A and 0.75 ˚A (1 ˚A= 10−10m). Then most likely,

(1) P = 41Nb; Q = 29Cu
(2) P = 29Cu; Q = 47Ag
(3) P = 29Cu; Q = 41Nb
(4) P = 41Nb; Q = 27Co

Solution :- wavelength of emitted x rays is given by
$\bold{\nu\propto Z^2}$
Here, ν is the frequency of x rays and Z is atomic number
We also know, wavelength = speed of light/frequency
e.g., λ = c/ν ∴ ν = c/λ
so, $\bold{\frac{1}{\lambda}\propto Z^2}$
$\implies\bold{\lambda\propto\frac{1}{Z^2}}$

∴ $\bold{\frac{\lambda_1}{\lambda_2}=\frac{Z_2^2}{Z_1^2}}$
Here, λ₁ = 1.5 A° and λ₂ = 0.75A°
∴ $\bold{\frac{\lambda_1}{\lambda_2}}$ = 1.5/0.75 = 2
so, 2 = Z₂²/Z₁²
⇒ √2 = Z₂/Z₁
⇒ 1.414 = Z₂/Z₁

Now, check all options which one follow the given condition .
Option (1) 29/41 ≠ 1.414
Option (2) 47/29 = 1.62 ≠ 1.414
Option (3) 41/29 = 1.4137 ≈ 1.414 , this is the correct answer.
Option (4) 27/41 ≠ 1.414

Hence, option (3) is correct