If the radius of the innermost Bohr orbit of a hydrogen atom is 53 pm , what is the radius of the second allowed Bohr orbit of a singly ionised helium atom ( He ⁺ )?

Step-by-step solution

The radius of the n^ th Bohr orbit for a hydrogen-like ion is given by: r_n = r₁ ( n^2 Z ) where r₁ is the radius of the innermost orbit of the hydrogen atom, n is the principal quantum number, and Z is the atomic number. For a singly ionised helium atom ( He ⁺ ), Z = 2 . For the second allowed orbit, n = 2 . Substituting the values: r₂ = 53 2^2 2 r₂ = 53 2 = 106 pm Answer: 106 pm