Using Bohr's model, find the ratio of magnetic fields produced due to the motion of the electron in the 1st and 4th orbit of a hydrogen atom.

An electron revolving around the nucleus behaves like a current loop.

The magnetic field at the centre of the orbit is:

B = μ₀I / 2r

Current:

I = e/T

For Bohr orbits:

r_n ∝ n²

v_n ∝ 1/n

Current:

I ∝ v/r

∝ (1/n)/(n²)

∝ 1/n³

Therefore:

B ∝ I/r

∝ (1/n³)/(n²)

∝ 1/n⁵

Hence:

B₁ : B₄

= 1 : (1/4⁵)

= 4⁵ : 1

= 1024 : 1

Final Answer

1024 : 1