Calculate the energy associated with the second orbit of $\mathrm{Li}^{+}$and find it's radius?

Calculate the energy associated with the second orbit of $\mathrm{Li}^{+}$and find it's radius?
  1. $4.905 \times 10^{-19} \mathrm{~J}, 0.0705 \mathrm{~nm}$
  2. $4.905 \times 10^{-20} \mathrm{~J}, 0.0705 Å$
  3. $4.905 \times 10^{-17} \mathrm{~J}, 0.0705 Å$
  4. $4.905 \times 10^{-18} \mathrm{~J}, 0.0705 \mathrm{~nm}$

Solution

Energy associated with second Bohr's orbit is $ \begin{aligned} E & =-13.6 \mathrm{Z}^2 / n^2 \\ E & =-13.6 \times 3^2 / 2^2 \\ E & =-30.6 \mathrm{eV} \\ & =-30.6 \times 1.6 \times 10^{-19} \\ & =4.905 \times 10^{-18} \mathrm{~J} \end{aligned} $ Radius of second Bohr's orbit in $\mathrm{Li}^{+}$is given by $ \begin{aligned} R & =0.529 n^2 / Z \\ R & =0.529 \times 2^2 / 3 \\ R & =0.7053 Å=0.0705 \mathrm{~nm} \end{aligned} $ Hence, the correct option is (4)

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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