NEET2026PhysicsAtomic PhysicsActual
In the first excited state of hydrogen atom, the energy of its electron is -3.4 eV. The radial distance of the electron from the hydrogen nucleus in this case 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 )
Options
- A2.1 10⁻⁹ m
- B2.1 10⁻⁸ m
- C2.1 10⁻¹⁰ m
- D2.1 10⁻¹¹ m
Correct answer
C. 2.1 10⁻¹⁰ m
Step-by-step solution
The total energy of an electron in a hydrogen atom is given by E = - 1 4 ₀ e^2 2r Substituting the given values: -3.4 1.6 10⁻¹⁹ = - 9 10^9 (1.6 10⁻¹⁹)^2 2r r = 9 10^9 1.6 10⁻¹⁹ 2 3.4 r = 14.4 10⁻¹⁰ 6.8 r 2.117 10⁻¹⁰ m This is approximately 2.1 10⁻¹⁰ m. Answer: 2.1 10⁻¹⁰ m