The energy of an electron in the first Bohr o | vedclass

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(D) The energy of an electron in the $n^{th}$ orbit is given by the formula $E_n = -2.18 	imes 10^{-18} 	imes \frac{Z^2}{n^2} \ J$.For a hydrogen at

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$1/9$ th of this value

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(D) The energy of an electron in the $n^{th}$ orbit is given by the formula $E_n = -2.18 	imes 10^{-18} 	imes \frac{Z^2}{n^2} \ J$.For a hydrogen atom,$Z = 1$.Therefore,$E_n \propto \frac{1}{n^2}$.For the first orbit $(n_1 = 1)$,$E_1 = -2.18 	imes 10^{-18} \ J$.For the third orbit $(n_3 = 3)$,$E_3 = E_1 	imes \frac{n_1^2}{n_3^2} = E_1 	imes \frac{1^2}{3^2} = \frac{E_1}{9}$.Thus,the energy in the third Bohr orbit is $1/9$ of the energy in the first Bohr orbit.

The energy of an electron in the first Bohr orbit of hydrogen atom is $-2.18 \times 10^{-18} \ J$. Its energy in the third Bohr orbit is $........$.

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