Question

In Bohr model of hydrogen atom, calculate:

1. the radius of the innermost electron orbit, and
2. the speed of electron in this orbit.

Answer 1

The Bohr model assumes that electrons orbit the nucleus in specific quantized orbits where the angular momentum is an integral multiple of `h/(2π)`.

Using standard constants:

ϵ₀ = 8.854 × 10⁻¹² C²/Nm²

h = 6.626 × 10⁻³⁴ Js

m = 9.1 × 10⁻³¹ kg

e = 1.6 × 10⁻¹⁹ C

a. Radius of n th orbit (r_n) = `(epsilon_0 n^2 h^2)/(pi m e^2)`

r₁ = `((8.854 xx 10^-12) * 1^2 * (6.626 xx 10^-34)^2)/(3.14 * (9.1 xx 10^-31) * (1.6 xx 10^-19)^2)`

= 0.529 × 10⁻¹⁰ m

= 0.529 Å

b. Speed in n th orbit (v_n) = `e^2/(2 epsilon_0 n h)`

v₁ = `((1.6 xx 10^-19)^2)/((2 * (8.854 xx 10^-12) * 1 * (6.626 xx 10^-34)`

v₁ ≈ 2.18 × 10⁶ m/s