The wavelength of Kα and Lα X-Rays of a material are 20 pm and 140

Question

The wavelength of

K_{α}

and

L_{α}

X-Rays of a material are 20 pm and 140 pm respectively. Find the wavelength of

K_{β}

X-Ray of the material.

Options:

A . 12.5 pm

B . 15.5 pm

C . 17.5 pm

D . 19.5 pm

Answer: Option C
:
C
For the wavelength of

K_{α}

x-rays;

\frac{h c}{λ_{1}}

E_{K} - E_{L}

for the wavelength of

L_{α}

x-rays;

\frac{h c}{λ_{2}}

E_{L} - E_{M}

or the wavelength of

K_{β}

x-rays;

\frac{h c}{λ_{3}}

E_{K} - E_{M}

Now,
If we add the first two equation we get :

h c (\frac{1}{λ_{1}} + \frac{1}{λ_{2}}) = E_{K} - E_{M}

Now from equations iii) and iv)

\frac{h c}{λ_{3}} = h c (\frac{1}{λ_{1}} + \frac{1}{λ_{2}}) .

We get;

\frac{1}{λ_{3}} = (\frac{1}{λ_{1}} + \frac{1}{λ_{2}}) .

Or,

\frac{1}{λ_{3}} = (\frac{1}{20} + \frac{1}{140}) p m^{- 1}

Or,

λ_{3} = \frac{2800}{160} p m .

Or,

λ_{3}

= 17.5 pm

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