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Chemistry Question on Developments Leading to the Bohr’s Model of Atom

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.

Answer

Energy (E) of the nth Bohr orbit of an atom is given by,
En=−(2.18×10−18)Z2n2E_n = \frac {-(2.18×10^{-18})Z^2}{n^2}
Where,
Z = atomic number of the atom
Ground state energy = - 2.18 × 10-11 ergs
= - 2.18 × 10-11× 10-7 J
= - 2.18 × 10-18 J
Energy required to shift the electron from n = 1 to n = 5 is given as:
ΔE=E5−E1ΔE = E_5-E_1
ΔE=−(2.18×10−18)(1)2(5)2−(−2.18×10−18)ΔE= \frac {-(2.18×10^{-18}) (1)^2}{(5)^2} - (- 2.18×10^{-18})

ΔE=(2.18×10−18)[1−125]ΔE= (2.18×10^{-18}) [1 - \frac {1}{25}]

ΔE=(2.18×10−18)(2425)ΔE = (2.18×10^{-18}) (\frac {24}{25})
ΔE=2.0928×10−18JΔE = 2.0928×10^{-18} J
Wavelength of emitted light = hcE\frac {hc}{E}

= (6.626×10−34)(3×108)(2.0928×10−18)\frac {(6.626 × 10^{-34}) (3×10^8)}{(2.0928×10^{-18})}
= 9.498×10−18m9.498×10^{-18} m