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NCERT Class XI Chemistry Structure of Atom Solutions

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Question : 7 of 67
Marks: +1, -0
Calculate the wavelength, frequency and wavenumber of a light wave whose time period is 2.0 × 1010s10^{-10}\,\mathrm{s}.
Solution:  
Frequency of a light wave
(υ) = 1Time period\frac{1}{\text{Time period}} = 12.0×1010\frac{1}{2.0 \times 10^{-10}} = 5 × 109s110^9\,\mathrm{s}^{-1}
Wavelength of light wave (λ) = cυ\frac{c}{\upsilon} = 3×1085×109\frac{3 \times 10^8}{5 \times 10^9} = 6.0 × 102m10^{-2}\,\mathrm{m}
Wavenumber of light wave (v)\left(\overset{-}{v}\right) = 1λ\frac{1}{\lambda} = 16.0×102\frac{1}{6.0 \times 10^{-2}} = 16.6 m1\mathrm{m}^{-1}
Therefore, wavelength, frequency and wavenumber of the light wave are 6.0 × 10210^{-2} m, 5 × 109s110^9\,\mathrm{s}^{-1} and 16.6 m1\mathrm{m}^{-1} respectively.
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