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





Q.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 –2.18×10-11 ergs.

 

 

Answer:-
1erg = 10-7 J
As ground state electronic energy is  –2.18×10-11 ergs, this means that En = -21.8×10-11/n2 ergs.
 ΔE = E5 – E= 2.18×10-11 (1/1 1/52) = 2.18×10-11(24/25) = 2.09×10-11 ergs = 2.09×10-18 J
When electron returns to ground state (n=1), energy emitted = 2.09×10-11 ergs.
As, E = hν = hc/λ
⇒ λ = hc/E = (6.626×10-27 erg sec) (3.0×1010 cm s-1)/2.09×10-11 ergs
        = 9.51×10-6 cm = 951×10-8 cm = 951 Å