Question

Calculate the energy of the electron in the ground state of the hydrogen atom. Express it in joule and in eV.

Answer 1

Data: m = 9.11 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C, h = 6.63 ×  10⁻³⁴ J.s, ε₀ = 8.85 × 10⁻¹² C²/N.m²

The energy of electron in nth Bohr orbit is

E_n = `-1/(n^2)(me^4)/(8ε_0^2h^2)`

For the ground state, n = 1.

∴ E₁ = `-1 × ((9.11 × 10^-31)(1.6 × 10^-19)^4)/(8(8.85 × 10^-12)^2(6.63 × 10^-34)^2)`

= − 2.168 × 10⁻¹⁸ J

= `(-2.168 × 10^-18 J)/(1.6 × 10^-19 J//eV)`

= − 13.55 eV