The electron energy in hydrogen atom is given by En= (–2.18 × 10–18)/n2J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?


Given:

Electron energy in Hydrogen atom En = [(–2.18 × 10–18)/n2] J


Energy for first state, E1 = [–2.18 × 10–18]/12


= –2.18 × 10–18 J


Energy for second state, E2 = [–2.18 × 10–18]/22


= –0.5465 × 10–18 J


By Planck’s relation we have,


Energy, E = h×v


But we know v = [c] / [λ]


Where


c = Speed of Light


v= Frequency


λ = Wavelength


So, E = hc /λ


λ = hc / E


= [[6.626×10-34] × [3×108]] / [0.5465 × 10–18]


= [1.9878×10-25] / [0.5465 × 10–18]


= 3.637×10-7 m


Therefore, the wavelength is 3.64×10-7 m


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