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Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is 9/x×10⁻¹⁰ m. The value of x is ______. (1 eV=1.6×10⁻¹⁹ J, 1/(4πε₀)=9×10⁹ Nm²/C² and electronic charge =1.6×10⁻¹⁹ C)

Asked in JEE Main 6th April 2nd Shift 2023 · Energy levels and ionisation

Answer: 16

Step-by-step solution

Binding energy =(ke²)/(2r)

r=(9×10⁹×(1.6×10⁻¹⁹)²)/(2×12.8×1.6×10⁻¹⁹)=(1.44×10⁻⁹)/(25.6)=5.625×10⁻¹¹ m

=9/(16)×10⁻¹⁰ m

→ 16

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