In the simplified K-series model with screening constant 1, an element has atomic number Z = 21. The approximate Kβ photon energy is calculated from E(Kβ) = 13.6(Z-1)²[1-1 ÷ 3²] eV. Which value is closest?
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Question

In the simplified K-series model with screening constant 1, an element has atomic number Z = 21. The approximate Kβ photon energy is calculated from E(Kβ) = 13.6(Z-1)²[1-1 ÷ 3²] eV. Which value is closest?

Options

G1 Physics · Accepted Answer

For Z = 21, Z−1 = 20. For Kβ radiation, E(Kβ) = 13.6×20²×[1−1 ÷ 9] = 13.6×400×8 ÷ 9. Thus, E(Kβ) ≈ 4835.6 eV ≈ 4.84 keV. Correct option: C.

In the simplified K-series model with screening constant 1, an element has atomic number Z = 21. The approximate Kβ photon energy is calculated from E(Kβ) = 13.6(Z−1)²[1−1 ÷ 3²] eV. Which value is closest?