Experimentally it is found that 12.8 eV energy is required to sep… — Solution | JEE Physics

NVAMediumJEE 2023Bohr's Model & Hydrogen Spectrum

Experimentally it is found that $12.8 \, \text{eV}$ 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 $\dfrac{9}{x} \times 10^{-10} \, \text{m}$ . The value of $x$ is

Answer

Correct answer:16

Step-by-step solution

Standard Method

Given: Energy required to separate the hydrogen atom into a proton and an electron is $12.8 \, \text{eV}$ .

Find: The value of $x$ in the orbital radius $\dfrac{9}{x} \times 10^{-10} \, \text{m}$ .

The solution only states that the correct answer is $16$ .

Therefore, the value of $x$ is $16$ .

Common mistakes

Using the given $12.8 \, \text{eV}$ directly as the orbital radius is incorrect because it is an energy value, not a length. First relate the binding energy to the hydrogen atom model, then compare with the given radius form.
Confusing ionization energy with kinetic energy of the electron is incorrect because the energy required to separate the atom corresponds to the binding energy magnitude. Use the hydrogen ground-state relation before extracting the radius.

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