Question
If the series limit frequency of the Lyman series is $${\nu _1},$$ then the series limit frequency of the $$P$$-fund series is :
A.
$$25\,{\nu _L}$$
B.
$$16\,{\nu _L}$$
C.
$$\frac{{{\nu _L}}}{{16}}$$
D.
$$\frac{{{\nu _L}}}{{25}}$$
Answer :
$$\frac{{{\nu _L}}}{{25}}$$
Solution :
$$\eqalign{
& h{\nu _L} = {E_\infty } - {E_1}\,......\left( {\text{i}} \right) \cr
& h{\nu _f} = {E_\infty } - {E_5}\,......\left( {{\text{ii}}} \right) \cr
& E\,\infty \,\frac{{{z^2}}}{{{n^2}}} \Rightarrow \frac{{{E_5}}}{{{E_1}}} = {\left( {\frac{1}{5}} \right)^2} = \frac{1}{{25}} \cr
& {\text{Equation}}\,\frac{{\left( {\text{i}} \right)}}{{\left( {{\text{ii}}} \right)}} \Rightarrow \frac{{h{\nu _L}}}{{h{\nu _f}}} = \frac{{{E_1}}}{{{E_5}}} \cr
& \Rightarrow \frac{{{\nu _L}}}{{{\nu _f}}} = \frac{{25}}{1} \Rightarrow {\nu _f} = \frac{{{\nu _L}}}{{25}} \cr} $$