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Which of the following relations for the hydrogen atom is incorrect?

1. E1 < E2 < E3, where En is the energy of the nth shell
2. The number of spectral lines in the Balmer series equals n2 - 2
3. The radius of the nth shell is given by rₙ = 0.529 * n² / Z Angstrom
4. The wave number is given by: nu_bar = R_H * Z² * (1/n1² - 1/n2²)

Correct answer: The radius of the nth shell is given by rₙ = 0.529 * n² / Z Angstrom

Solution

The correct Bohr radius formula is rₙ = 0.529 * n² / Z Angstrom (or equivalently 52.9 * n² / Z pm). The option states pm in place of Angstrom, making the numerical value off by a factor of 100.

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