A) \[{{n}^{0}}\]
B) \[{{n}^{-1}}\]
C) \[{{n}^{-2}}\]
D) \[{{n}^{-3}}\]
Correct Answer: D
Solution :
[d]: According to Bohr?s theory of hydrogen atom \[\frac{1}{\lambda }=R{{Z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\] \[\upsilon =\frac{c}{\lambda }=Rc{{Z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\] \[\therefore \]\[\upsilon \propto \left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)=\frac{n_{2}^{2}-n_{1}^{2}}{n_{1}^{2}n_{2}^{2}}\] \[\upsilon \propto \left( \frac{{{n}^{2}}-{{(n-1)}^{2}}}{{{n}^{2}}{{(n-1)}^{2}}} \right)=\frac{2n-1}{{{n}^{2}}{{(n-1)}^{2}}}\] When \[n>>1,\] \[\upsilon \propto \frac{2n}{{{n}^{4}}},\]i.e.,\[\upsilon \propto \frac{1}{{{n}^{3}}}\]or\[\upsilon \propto {{n}^{-3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
