The Kα frequency of element B is 16 ÷ 9 times that of element A. Element A has atomic number 10. Assuming the same screening constant in Moseley's law, find the atomic number of B.
Physics · Atomic Structure and X-rays · x-rays and its types
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Question

The Kα frequency of element B is 16 ÷ 9 times that of element A. Element A has atomic number 10. Assuming the same screening constant in Moseley's law, find the atomic number of B.

G1 Physics · Accepted Answer

Moseley's law gives ν ∝ (Z−1)². Thus, 16 ÷ 9 = (Z(B)−1)² ÷ (10−1)² = (Z(B)−1)² ÷ 9². Taking square roots: 4 ÷ 3 = (Z(B)−1) ÷ 9. Therefore, Z(B)−1 = 12, so Z(B) = 13. Hence the answer is 13.