For a He ^+ ion, the distance of the electron from the nucleus in the third Bohr orbit is 238.05 pm . What will be the corresponding distance for an electron revolving in the fifth Bohr orbit of a B ⁴⁺ ion?

Step-by-step solution

The radius of the n -th Bohr orbit for a hydrogen-like species is given by: r_n = r₀ n^2 Z For the He ^+ ion ( Z = 2 ) in the third orbit ( n = 3 ): r_ He ^+ = r₀ 3^2 2 = 238.05 pm r₀ = 238.05 2 9 = 52.9 pm For the B ⁴⁺ ion ( Z = 5 ) in the fifth orbit ( n = 5 ): r_ B ⁴⁺ = r₀ 5^2 5 = 5 r₀ Substituting the value of r₀ : r_ B ⁴⁺ = 5 52.9 = 264.5 pm Answer: 264.5 pm