What are the energy of the second Bohr orbit of Be ³⁺ and the radius of the third Bohr orbit of He ⁺ respectively? [Given: R _ H = 2.18 10⁻¹⁸ J , a ₀ = 52.9 pm ]

Step-by-step solution

The energy of the n -th Bohr orbit for a hydrogen-like species is given by E_n = -R_H Z^2 n^2 For Be ³⁺ , the atomic number Z = 4 . For the second orbit, n = 2 . E₂ = -2.18 10⁻¹⁸ 4^2 2^2 = -2.18 10⁻¹⁸ 4 = -8.72 10⁻¹⁸ J The radius of the n -th Bohr orbit is given by r_n = a₀ n^2 Z For He ⁺ , the atomic number Z = 2 . For the third orbit, n = 3 . r₃ = 52.9 3^2 2 = 52.9 4.5 = 238.05 pm Answer: -8.72 10⁻¹⁸ J and 238.05 pm