Experimentally, 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. The orbital radius of the electron is (9/x) × 10⁻¹⁰ m. Find x. [1 eV = 1.6 × 10⁻¹⁹ J, 1/(4πε₀) = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C]
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 2 Evening Shift

Question

Experimentally, 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. The orbital radius of the electron is (9/x) × 10⁻¹⁰ m. Find x. [1 eV = 1.6 × 10⁻¹⁹ J, 1/(4πε₀) = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C]

Physics · Circular Motion

JEE Mains 6 April 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

The ionization energy of the hydrogen atom is equal to the magnitude of its total ground-state energy: E = ke²/(2r) Therefore, r = ke²/(2E) Given: E = 12.8 eV = 12.8×1.6×10⁻¹⁹ J k = 9×10⁹ N m² C⁻² e = 1.6×10⁻¹⁹ C Substituting: r = [9×10⁹ × (1.6×10⁻¹⁹)²] / [2×12.8×1.6×10⁻¹⁹] = 5.625×10⁻¹¹ m = (9/16)×10⁻¹⁰ m Hence x = 16. Final value: 16