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  • As per the Bohr model, find the possible values of principal quantum numbers <img alt="\mathrm{\left(n_1\, \& \, n_2\right) }" src="/latex-image/?%5Cmathrm%7B%5Cleft%28n_1%5C%2C%20%5C%26%20%5C%

As per the Bohr model, find the possible values of principal quantum numbers \mathrm{\left(n_1\, \& \, n_2\right) } in an electron transition of hydrogen atom from \mathrm{n_{1}} to \mathrm{n_{2}}. The time period of an election in the initial state is 27 times the time period of electron in the final state.

Option: 1

\mathrm{n_1=6 ; n_2=3}


Option: 2

\mathrm{n_1=6 ; n_2=2}


Option: 3

\mathrm{n_1=8 ; n_2=2}


Option: 4

\mathrm{n_1=n_2=1}


Answers (1)

best_answer

\mathrm{T =\frac{2 \pi r}{V} }
\mathrm{V =\frac{n h}{2 \pi m r} }
\mathrm{\therefore T =\frac{2 \pi r}{n h / 2 \pi m r}=\frac{4 \pi^2 m r^2}{n h} }
\mathrm{T=\frac{r^2}{n} }

\mathrm{but \: r\, \alpha \, n^2}
\mathrm{\therefore T \propto \frac{1}{n^3}}
\mathrm{\left(\frac{T_1}{T_2}\right)=\left(\frac{n_1}{n_2}\right)^3}
\mathrm{T_1=27 T_2 }
\mathrm{\left(\frac{n_1}{n_2}\right)^3=27 }
\mathrm{\frac{n_1}{n_2}=3}
\mathrm{\therefore \text{in given values,\: } n_1=6 ; n_2=2}

Posted by

SANGALDEEP SINGH

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