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The kinetic energy of an electron in the $n$-th Bohr orbit of a hydrogen atom is related to its total energy $E_n$ by:
A$E_k = E_n$
B$E_k = 2E_n$
C$E_k = -E_n$
D$E_k = -E_n / 2$
Answer & Solution
Correct answer: C. $E_k = -E_n$
For the Bohr atom the magnitudes of kinetic and total energy are equal but opposite in sign: $E_k = +13.6 Z^2/n^2\,\text{eV}$ and $E_n = -13.6 Z^2/n^2\,\text{eV}$. Hence $E_k = -E_n$. Equivalently $E_k = -E_n$ and $U = 2E_n$, with $U + E_k = E_n$.
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