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NCERT Class XII Chapter
Atoms
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Question : 6 of 18
Marks: +1, -0
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
Solution:  
Energy of an electron in the nth orbit of H-atom, EnE_n = - 13.6n2\frac{13.6}{n^2} eV
Energy in the ground (n = 1) level, E1E_1 = - 13.612\frac{13.6}{1^2} = - 13.6 eV
Energy in the fourth (n = 4) level, E4E_4 = - 13.642\frac{13.6}{4^2} = - 0.85 eV
Energy radiated during emission
ΔE = E4−E1E_4 - E_1 = –0.85 – (–13.6) = 12.75 eV
As hυ = ΔE
∴ Frequency, υ = ΔEh\frac{\Delta E}{h} = 12.75×1.6×10−196.6×10−34\frac{12.75 \times 1.6 \times 10^{-19}}{6.6 \times 10^{-34}} = 3.078 × 101510^{15} Hz
Wavelength, λ = cυ\frac{c}{\upsilon} = 3×1083.078×1015\frac{3 \times 10^8}{3.078 \times 10^{15}} = 0.9744 × 10−710^{-7} m = 974.4 Å
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