In the simplified hydrogen-like K-series model, the same effective nuclear charge is used for the Kα and Kβ lines of one element. If ν(Kβ) ÷ ν(Kα) = N ÷ 27, find N.
Physics · Atomic Structure and X-rays · x-rays and its types
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Question

In the simplified hydrogen-like K-series model, the same effective nuclear charge is used for the Kα and Kβ lines of one element. If ν(Kβ) ÷ ν(Kα) = N ÷ 27, find N.

G1 Physics · Accepted Answer

For Kα radiation, ν(Kα) ∝ 1−1 ÷ 2² = 1−1 ÷ 4 = 3 ÷ 4. For Kβ radiation, ν(Kβ) ∝ 1−1 ÷ 3² = 1−1 ÷ 9 = 8 ÷ 9. Therefore, ν(Kβ) ÷ ν(Kα) = (8 ÷ 9) ÷ (3 ÷ 4) = (8 ÷ 9)×(4 ÷ 3) = 32 ÷ 27. Hence N = 32.