In a simplified Moseley-Bohr model for K-series X-rays, the screening constant is taken as 1. For an element with atomic number Z = 11, estimate the Kα photon energy using E(Kα) = 13.6(Z−1)²[1−1 ÷ 2²] eV. If the result is N eV, find N.
Physics · Atomic Structure and X-rays · x-rays and its types
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Question

In a simplified Moseley-Bohr model for K-series X-rays, the screening constant is taken as 1. For an element with atomic number Z = 11, estimate the Kα photon energy using E(Kα) = 13.6(Z−1)²[1−1 ÷ 2²] eV. If the result is N eV, find N.

Physics · Atomic Structure and X-rays · x-rays and its types

G1 Physics · Accepted Answer

For Z = 11, Z−1 = 10. For Kα radiation, the electron falls from the second shell to the first shell, so E(Kα) = 13.6(Z−1)²[1−1 ÷ 4]. Substitute: E(Kα) = 13.6×10²×3 ÷ 4 = 13.6×100×0.75 = 1020 eV. Hence N = 1020.