For a hydrogen atom excited to the n = 2 state, the average lifetime is 10⁻⁸ ext s . Determine the average number of revolutions completed by the electron before it transitions to the ground state.

Step-by-step solution

The time period of an electron in the n^ th orbit of a hydrogen atom is given by T_n = 2 r_n v_n . The radius of the n^ th orbit is r_n = 0.529 10⁻¹⁰ n^2 Z m . The velocity of the electron in the n^ th orbit is v_n = 2.18 10^6 Z n m/s . For a hydrogen atom, Z = 1 . In the excited state n = 2 , the radius and velocity are: r₂ = 0.529 10⁻¹⁰ 4 = 2.116 10⁻¹⁰ m v₂ = 2.18 10^6 2 = 1.09 10^6 m/s Substituting these values to find the time period T₂ : T₂ = 2 3.14 2.116 10⁻¹⁰ 1.09 10^6 1.22 10⁻¹⁵ s The average lifetime of th