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  • What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state

2.18    What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is -2.18\times 10^{-11}\ \textup{ergs}.

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The ground state energy:

E_{1} = -2.18\times10^{-11}\ ergs

       = -2.18\times10^{-11}\times10^{-7} J

       = -2.18\times10^{-18} J

The energy required to shift the electron from the first Bohr orbit to the fifth Bohr orbit is:

\triangle E = E_{5}-E_{1}

And the expression for the energy of an electron is given by:

E_{n} =-\frac{2n^2me^4Z^2}{n^2h^2}

where m is mass of an electron, Z is the atomic mass of an atom, e is a charge of an electron, and h is the Planck's constant.

Now, substituting the values in the equation, we get

=-\frac{(2.18\times10^{-18})(1)^2}{(5)^2} - (-2.18\times10^{-18})

=(2.18\times10^{-18})\left [ 1-\frac{1}{25} \right ]

=(2.18\times10^{-18}) \left ( \frac{24}{25}\right ) = 2.0928\times10^{-18}J

Hence, the wavelength of the emitted light will be:

\lambda = \frac{hc}{E} = \frac{(6.626\times10^{-34}Js)(3\times10^8m/s)}{(2.0928\times10^{-18}J)}

= 9.498\times10^{-8}\ m

Posted by

Divya Prakash Singh

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