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 light emitted when the electron returns to the ground state? The ground state electronic energy is – 2.18 × 11-11 ergs.
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 light emitted when the electron returns to the ground state? The ground state electronic energy is – 2.18 × 11-11 ergs.
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1 Answer
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Step I: calculation of energy required
Energy of electron (En) = (- 2.18 x 10-11ergs) / n2= (- 2.18 x 10-18 J) / n2
Energy in Bohr’s 1st orbit (E1) = (- 2.18 x 10-18 J) / 12
Energy in Bohr’s 5th orbit (E1) = (- 2.18 x 10-18 J) / 52
Therefore, energy required (ΔE) = E5 – E1 = [ (- 2.18 x 10-18 J) / 25] – [ (- 2.18 x 10-18 J) / 1]
= 2.18 x 10-18 (1 – 1/25) J
= 2.18 x 10-18 x 24 / 25
= 2.09 x 10-18 J
Step II: Calculation of wavelength of light emitted
λ = hc / ΔE = (6.626 x 10-34 J s) x (3 x 108 ms-1) / (2.09 x 10-18 J) = 9.50 x 10-8 m = 950
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