The potential energy of an electron in a specific orbit of a singly ionized helium atom ( He^+ ) is -27.2 eV. The radial distance of this orbit from the nucleus is approximately: (Take 1 eV = 1.6 10⁻¹⁹ J, e = 1.6 10⁻¹⁹ C and 1 4 ₀ = 9 10⁹ N m ^2 /C ^2 )

Step-by-step solution

The potential energy of an electron in a hydrogen-like atom is given by: U = - 1 4 ₀ Z e^2 r For a singly ionized helium atom ( He^+ ), Z = 2 . The given potential energy is U = -27.2 eV. Converting the potential energy to Joules: U = -27.2 1.6 10⁻¹⁹ J Substituting the values into the potential energy formula: -27.2 1.6 10⁻¹⁹ = -9 10^9 2 (1.6 10⁻¹⁹)^2 r Solving for r : r = 9 10^9 2 1.6 10⁻¹⁹ 27.2 r = 28.8 10⁻¹⁰ 27.2 r 1.0588 10⁻¹⁰ m Rounding to two decimal places, we get: r 1.06 10⁻¹⁰ m Answer: 1.06 10⁻¹⁰ m