Question 39.43: In the ground state of the hydrogen atom, the electron has a......

Fundamentals of Physics Extended – Instructor’s Solutions Manual [1360823]

In the ground state of the hydrogen atom, the electron has a total energy of -13.6 eV. What are (a) its kinetic energy and (b) its potential energy if the electron is one Bohr radius from the central nucleus?

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(a) and (b) Letting $a=5.292 \times 10^{-11}$ m be the Bohr radius, the potential energy becomes

$U=-\frac{e^2}{4 \pi \varepsilon_0 a}=\frac{( 8.99 \times 10^9\, N \cdot m ^2 / C ^2 )( 1.602 \times 10^{-19} C) ^2}{5.292 \times 10^{-11} \,m }=-4.36 \times 10^{-18}\, J =-27.2\, eV$ .

The kinetic energy is K = E – U = (– 13.6 eV) – (– 27.2 eV) = 13.6 eV.

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