Dimensional formula of Bohr magneton

How to get the dimensional formula of Bohr magneton

1. Start from the definition: Bohr magneton = elementary charge × plancks constant / electron mass.
2. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
3. elementary charge = electric charge, so elementary charge is [T A] = [T A].
4. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
5. energy = mass × velocity², so energy is [M] × [L T^-1]² = [M L² T^-2].
6. Planck's constant = energy × time, so Planck's constant is [M L² T^-2] × [T] = [M L² T^-1].
7. electron mass = mass, so electron mass is [M] = [M].
8. Put in the dimension of each part: [T A] × [M L² T^-1] / [M].
9. Add the powers of each base quantity: [L² A].

Quantities with the dimensions [L² A]

• Magnetic moment

Equal dimensions do not make them the same quantity. Compare Bohr magneton with the others in the full grid.

Three questions on Bohr magneton

Related quantities

• G Gravitational constant [M⁻¹ L³ T⁻²]
• c Speed of light [L T⁻¹]
• h Planck's constant [M L² T⁻¹]
• ħ Reduced Planck's constant (h-bar) [M L² T⁻¹]
• k Boltzmann constant [M L² T⁻² K⁻¹]
• R Universal gas constant [M L² T⁻² K⁻¹ mol⁻¹]