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 ____.
- One third of this value
- \(\frac{1}{9}\) th of this value
- Three times of this value
- \(\frac{1}{27}\) of this value
The Correct Option is B
Solution and Explanation
The energy of an electron in the \( n \)-th Bohr orbit is given by the formula: \[ E_n = \frac{-13.6 \, \text{eV}}{n^2}. \] For the first orbit (\( n = 1 \)): \[ E_1 = \frac{-13.6}{1^2} = -13.6 \, \text{eV}. \] For the third orbit (\( n = 3 \)): \[ E_3 = \frac{-13.6}{3^2} = \frac{-13.6}{9} = -1.51 \, \text{eV}. \] Hence, the energy in the third orbit is \( \frac{1}{9} \) of the energy in the first orbit.
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