Two hydrogen-like atoms X and Y each have an A/Z ratio of 2. Atom Y is twice as heavy as atom X. The difference in photon energies for the first line of the Balmer series of X and Y is 17/3 eV. Find Zx² + Zy². (Ground state energy of hydrogen = -13.6 eV.)

Question

Accepted Answer

5. First Balmer line energy E = 13.6*Z²*5/36 eV. Difference |Ey - Ex| = 13.6*(5/36)*(Zy²-Zx²) = 17/3. With Zy = 2Zx: 3Zx² factor. Solving gives Zx = 1, Zy = 2. Zx² + Zy² = 1 + 4 = 5.

Two hydrogen-like atoms X and Y each have an A/Z ratio of 2. Atom Y is twice as heavy as atom X. The difference in photon energies for the first line of the Balmer series of X and Y is 17/3 eV. Find Zx² + Zy². (Ground state energy of hydrogen = -13.6 eV.)

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