Question

Calculate the radius of the first Bohr orbit in the hydrogen atom.

Answer 1

Data: ε₀ = 8.85 × 10⁻¹² C²/N.m², e = 1.6 × 10⁻¹⁹ C,

h = 6.63 × 10⁻³⁴ J.s, m = 9.1 × 10⁻³¹ kg

The radius of a Bohr orbit,

r = `(ε_0h^2n^2)/(πme^2)`

∴ `r_1 = (ε_0h^2)/(πme^2)` (for n = 1)

∴ `r_1 = (8.85 xx 10^-12 xx (6.63 xx 10^-34)^2)/(3.142 xx 9.1 xx 10^-31 xx (1.6 xx 10^-19)^2)`

= `(8.85 xx (6.63)^2 xx 10^-80)/(3.142 xx 9.1 xx 2.56 xx 10^-69)`

= 5.315 × 10⁻¹¹ m

This is the radius of the first Bohr orbit in the hydrogen atom.