Compare the orbital period of an electron in the fourth Bohr orbit of hydrogen with the period of an electron in the second orbit of He⁺. If T(H) ÷ T(He⁺) = N, find N.

Question

G1 Physics · Accepted Answer

For a hydrogen-like species, Tₙ ∝ n³ ÷ Z². For hydrogen: n = 4, Z = 1, so the proportional factor is 4³ ÷ 1² = 64. For He⁺: n = 2, Z = 2, so the proportional factor is 2³ ÷ 2² = 8 ÷ 4 = 2. Therefore, T(H) ÷ T(He⁺) = 64 ÷ 2 = 32. Hence N = 32.