The ratio of the difference between the 1^{st | vedclass

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(C) The energy of an electron in the $n^{th}$ Bohr orbit is given by $E_n = -\frac{13.6}{n^2} \ eV$.For $n=1$,$E_1 = -13.6 \ eV$.For $n=2$,$E_2 = -\fr

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$5.4$

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(C) The energy of an electron in the $n^{th}$ Bohr orbit is given by $E_n = -\frac{13.6}{n^2} \ eV$.For $n=1$,$E_1 = -13.6 \ eV$.For $n=2$,$E_2 = -\frac{13.6}{4} = -3.4 \ eV$.For $n=3$,$E_3 = -\frac{13.6}{9} \approx -1.51 \ eV$.The difference between $1^{st}$ and $2^{nd}$ orbits is $\Delta E_{2-1} = E_2 - E_1 = -3.4 - (-13.6) = 10.2 \ eV$.The difference between $2^{nd}$ and $3^{rd}$ orbits is $\Delta E_{3-2} = E_3 - E_2 = -1.51 - (-3.4) = 1.89 \ eV$.The ratio is $\frac{\Delta E_{2-1}}{\Delta E_{3-2}} = \frac{10.2}{1.89} \approx 5.4$.

The ratio of the difference between the $1^{st}$ and $2^{nd}$ Bohr orbits energy to the difference between the $2^{nd}$ and $3^{rd}$ Bohr orbits energy is:

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