The wavelength of characteristic X-ray K α -line emitted by a hydrogen like atom is 0.32 A ˚ . The wavelength of K β line emitted by the same element is :

λ K α 1 = R ( Z − 1 ) 2 ( 1 2 1 − 2 2 1 ) λ K β 1 = R ( Z − 1 ) 2 ( 1 2 1 − 3 2 1 ) λ K α λ K β = 8/9 3/4 = 32 27 λ K β = 0.32 × 32 27 = 0.27 A ˚

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PhysicsModern PhysicsX-raysMedium2 minQB

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The wavelength of characteristic X-ray $K_{α}$ -line emitted by a hydrogen like atom is $0.32 \overset{˚}{A}$ . The wavelength of $K_{β}$ line emitted by the same element is :

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Answer:

Solution:

$\frac{1}{λ _{K α}} = R (Z - 1)^{2} (\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}})$

$\frac{1}{λ _{K β}} = R (Z - 1)^{2} (\frac{1}{1 ^{2}} - \frac{1}{3 ^{2}}) \frac{λ _{K β}}{λ _{K α}} = \frac{3/4}{8/9} = \frac{27}{32} λ_{K β} = 0.32 \times \frac{27}{32} = 0.27 \overset{˚}{A}$

Subject:PhysicsTopic:Modern PhysicsSubtopic:X-rays

⏱ 2mℹ️ Source: QB

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