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The series limit of the Balmer series for hydrogen is 2700 Angstrom. Using Moseley's law for characteristic X-rays, find the atomic number Z of the element whose K-alpha line has wavelength 1.0 Angstrom. If Z = 10*p + 1, find the value of p.

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

From Balmer series limit: 1/lambda_B = R/4 => R = 4/lambda_B = 4/2700 Angstrom⁻¹. For K-alpha X-ray line: 1/lambda = R*(Z-1)²*(1 - 1/4) = R*(Z-1)²*3/4. Substituting: 1/1.0 = (4/2700)*(Z-1)²*(3/4) = 3*(Z-1)²/2700. So (Z-1)² = 2700/3 = 900 => Z-1 = 30 => Z = 31. Then 31 = 10p + 1 => 10p = 30 => p = 3.

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