The wavelength of the characteristic X-ray K α line emitted by a hydrogen-like element is 0.32 A ˚ . What would the wavelength of the K β line emitted by the same element? [Take b = 1 , for both K α \& K β ].

λ K α 1 = R ( 1 2 1 − 2 2 1 ) ( z − b ) 2 λ K β 1 = R ( 1 2 1 − 3 2 1 ) ( z − b ) 2 λ K α λ K β = 32 27 λ K β = 32 27 × 0.32 = 0.27 A ˚ .

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The wavelength of the characteristic X-ray $K_{α}$ line emitted by a hydrogen-like element is $0.32 \overset{˚}{A}$ . What would the wavelength of the $K_{β}$ line emitted by the same element? [Take $b = 1$ , for both $K_{α}$ \& $K_{β}$ ].

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Answer:

Solution:

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

$\frac{1}{λ _{K β}} = R (\frac{1}{1 ^{2}} - \frac{1}{3 ^{2}}) (z - b)^{2} \frac{λ _{K β}}{λ _{K α}} = \frac{27}{32} λ_{K β} = \frac{27}{32} \times 0.32 = 0.27 \overset{˚}{A} .$

Subject:PhysicsTopic:Modern PhysicsSubtopic:X-rays

⏱ 2mℹ️ Source: QB

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