The energy of an electron in the first Bohr orbit of hydrogen atom is -2.18 × 10⁻¹⁸ J. Its energy in the third Bohr orbit is ____________.

Solution

Chemistry ma’am · 3 steps

In hydrogen, energy goes as 1/n², so the third orbit gets 1/3² = 1/9 of the first orbit's energy.

1. Bohr energy formula. For hydrogen (Z = 1), the energy of the electron depends only on the orbit number n, and n² sits in the denominator.

   Eₙ = -(2.18 × 10⁻¹⁸)/n² J

2. Compare the orbits. Divide the third-orbit energy by the first-orbit energy: E₃/E₁ = 1²/3² = 1/9. So E₃ = (-2.18 × 10⁻¹⁸)/9 = -2.42 × 10⁻¹⁹ J.
3. So. The energy in the third orbit is 1/9th of the first-orbit value, which is option (c). It is less negative, so the electron is less tightly bound.

The idea to keep. Energy in a Bohr orbit varies as 1/n², radius as n², and speed as 1/n. Square the orbit number for energy before you compare two orbits.

Answer from the NTA final answer key. Solution by PrepWiser.