Question

The K,L and M energy levels of platinum lie roughly at 78,12 and 3keV respectively. The ratio of wavelength of K-alpha line to that of K-beta line in X-ray spectrum is?

Answer 1

Given that,

Energy level of platinum

$K=78\ eV$

$L=12\ eV$

$M = 3\ eV$

We need to calculate the wavelength of K-alpha line

Using formula of wavelength

$\dfrac{1}{\lambda_{\alpha}}=R(Z-1)^2(\dfrac{1}{1^2}-\dfrac{1}{2^2})$

Put the value into the formula

$\dfrac{1}{\lambda_{\alpha}}=R(78-1)^2(\dfrac{3}{4})$.....(I)

We need to calculate the wavelength of K-beta line

Using formula of wavelength

$\dfrac{1}{\lambda_{\beta}}=R(Z-1)^2(\dfrac{1}{1^2}-\dfrac{1}{3^2})$

Put the value into the formula

$\dfrac{1}{\lambda_{\beta}}=R(78-1)^2(\dfrac{8}{9})$.....(II)

We need to calculate the ratio of wavelength of K-alpha line to that of K-beta line in X-ray spectrum

Divided equation (II) by equation (I)

$\dfrac{\lambda_{\alpha}}{\lambda_{\beta}}=\dfrac{8\times4}{9\times3}$

$\dfrac{\lambda_{\alpha}}{\lambda_{\beta}}=\dfrac{32}{27}$

Hence, The ratio of wavelength of K-alpha line to that of K-beta line in X-ray spectrum is 32:27