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 × 10–11 ergs.The ground-state electron energy is –2.18 × 10–11 ergs.

Asked by Abhisek | 1 year ago |  77

1 Answer

Solution :-

Energy (E) associated with the nth Bohr orbit of an atom is:

\(E_{5}=\dfrac{-(2.18\times 10^{-18})Z^{2}}{(n)^{2}}\)

Where, Z denotes the atom’s atomic number

Ground state energy 

\(=-2.18 \times 10^{–11}\, ergs\\ =-2.18 \times 10^{–11} \times 10^{–7}\, J \\ =-2.18 \times 10^{–18} \, J\)

The required energy for an electron shift from n = 1 to n = 5 is:

\(\Delta E=E_{5}-E_{1}\\ \\ =[(\dfrac{-(2.18\times 10^{-18}\, J)(1)^{2}}{(5 )^{2}})-(-2.18\times 10^{-18})]\\ \\ =(2.18\times 10^{-18})[1-\dfrac{1}{25}]\\ \\ =(2.18\times 10^{-18})[\dfrac{24}{25}]\\ \\ =2.0928\times 10^{-18}\, J\)

The wavelength of the emitted light 

\(\dfrac{hc}{E }E=\dfrac{(6.626\times 10^{-34})(3\times 10^{8})}{(2.0928\times 10^{-18})}\\ \\ =9.498\times 10^{-8}\, m= 950 Å\)

Answered by Abhisek | 1 year ago

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