Question

Energy of an election in the second Bohr orbit is -3.4eV.calculate the energy of an election in the third Bohr orbit
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Answer 1

Given :

Energy of an electron in the second bohr orbit of hydrogen is -3.4eV

To Find :

Energy of an electron in the third bohr orbit.

Solution :

❒ According to bohr's atomic model, Energy of an electron in $\sf{n^{th}}$ orbit of atom is given by

$\bigstar\:\underline{\boxed{\bf{\red{E=-13.6\times\dfrac{Z^2}{n^2}}}}}$

• Z denoted atomic number
• n denotes principal quantum number of $\sf{n^{th}}$

In this question, atomic number is same so we can say that energy of an electron is inversely proportional to the square of principal quantum number of orbit.

$\sf:\implies\:\dfrac{E_1}{E_2}=\dfrac{n_2^2}{n_1^2}$

$\sf:\implies\:\dfrac{-3.4}{E_2}=\dfrac{3^2}{2^2}$

$\sf:\implies\:\dfrac{-3.4}{E_2}=\dfrac{9}{4}$

$\sf:\implies\:E_2=\dfrac{-3.4\times4}{9}$

$:\implies\:\underline{\boxed{\bf{\purple{E_2=-1.51\:eV}}}}$