Question 309: Atoms & Nuclei

Question

In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left( {n - 1} \right)$$. If $$n >  > 1,$$ the frequency of radiation emitted is proportional  to :

Accepted Answer

$$\Delta $$E $$ = 13.6{Z^2}\left[ {{1 \over {n_1^2}} - {1 \over {n_2^2}}} ight]$$
As $$\Delta $$E = h$$\upsilon $$
$$ \Rightarrow $$ $$\Delta $$E $$ \propto $$ $$\upsilon $$ $$ \propto $$ $$\left[ {{1 \over {n_1^2}} - {1 \over {n_2^2}}} ight]$$
Here n
1
= n - 1 and n
2
= n
$$ 	herefore $$ $$\upsilon $$ $$ \propto $$ $$\left[ {{1 \over {{{\left( {n - 1} ight)}^2}}} - {1 \over {{n^2}}}} ight]$$
$$ \Rightarrow $$ $$\upsilon $$ $$ \propto $$ $$\left[ {{{2n - 1} \over {{n^2}{{\left( {n - 1} ight)}^2}}}} ight]$$
[ As $$n >  > 1,$$ so we can assume n - 1 = n and 2n - 1 = 2n ]
$$ \Rightarrow $$ $$\upsilon $$ $$ \propto $$ $$\left[ {{{2n} \over {{n^2}{{\left( {n } ight)}^2}}}} ight]$$ $$ \propto $$ $$\left[ {{{2n} \over {{n^4}}}} ight]$$ $$ \propto $$ $$\left[ {{2 \over {{n^3}}}} ight]$$

Answer

$${1 \over n}$$

Answer

$${1 \over {{n^2}}}$$

Answer

$${1 \over {{n^{{3 \over 2}}}}}$$

Answer

$${1 \over {{n^3}}}$$

Atoms & Nuclei

In a hydrogen like atom electron make transition from an energy level with quantum number $n to another with quantum number \left( {n - 1} \right). If n > > 1,$ the frequency of radiation emitted is proportional to :

Choose the correct answer: