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What is the Bohr formula for the energy of an electron in the $n$-th orbit of a hydrogen-like atom of atomic number $Z$?

Study flashcard from the deck JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry.

Answer

$E_n = -13.6 \frac{Z^2}{n^2}\text{ eV}$.

Explanation

The orbital radius scales as $r_n = 0.529 \frac{n^2}{Z}\text{ \AA}$, and electron velocity scales as $v_n = 2.18 \times 10^6 \frac{Z}{n}\text{ m/s}$.

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