Determine the magnetic dipole moment associated with the motion of the electron in a hydrogen atom's ground state.

Step-by-step solution

The magnetic dipole moment of an electron in the n -th orbit of a hydrogen atom is given by M = e v r 2 . From Bohr's quantization condition, the angular momentum is L = m_e v r = n h 2 . Thus, v r = n h 2 m_e . Substituting this into the expression for magnetic moment: M = e 2 ( n h 2 m_e ) = n e h 4 m_e For the ground state, n = 1 . M = e h 4 m_e Substituting the standard values e = 1.6 10⁻¹⁹ C , h = 6.63 10⁻³⁴ J s , and m_e = 9.1 10⁻³¹ kg : M = 1.6 10⁻¹⁹ 6.63 10⁻³⁴ 4 3.14 9.1 10⁻³¹ M 9.27 10⁻²⁴ A m ^2