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The ratio of population of 2 energy level is 1.6 x 10-29. Find the wavelength of light emitted by spontaneous emission at 303 K. |
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Answer» Given \(\frac{N_2}{N_1}=1.6\times10^{-29}\) At the thermal equilibrium the ratio \(\frac{N_2}{N_1} \) = exp(\(\frac{-E_2-E_1}{KT}\)) \(\because\) E2 - E1 = \(\frac{hc}\lambda\) 1.6 x 10-29 = exp(\(\frac{-hc}{\lambda KT}\)) ln(1.6 x 10-29) = \(\frac{-hc}{\lambda KT}\) ln(1.6) - 29ln(10) = \(-\frac{hc}{\lambda kT}\) 0.470 - 29 x 2.30 = \(-\frac{hc}{\lambda KT}\) 0.470 - 66.7 = \(\frac{-hc}{\lambda KT}\) -66.23 = \(\frac{-hc}{\lambda KT}\) \(\lambda = \frac{6.626\times10^{-34}\times3\times10^8}{1.38\times10^{-23}\times303\times66.23}\) \(\lambda=\frac{19.87\times10^{-26}}{27693.41\times10^{-23}}\) ⇒ 0.000717 x 10-3 = 717 x 10-9 m |
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