c
\(\frac{1}{\lambda }\,\, = \,\,R\,\,\left[ {\frac{1}{{{1^2}}} - \frac{1}{{{n^2}}}} \right]\,\)

\(\frac{1}{{975\,\, \times \,\,{{10}^{ - 10}}}}\,\,\)

\( = \,\,\,1.1\,\, \times \,\,{10^7}\,\left[ {\frac{1}{{{1^2}}} - \frac{1}{{{n^2}}}} \right]\,\)

અથવા \(\,n\,\, = \,\,4\)

વર્ણપટ રેખાઓની સંખ્યા  \((N)\,\, = \,\,\frac{{n\,\,(n - 1)}}{2}\,\) 

\(\therefore\) \(\,\,N\,\, = \,\,\frac{{4\,\, \times \,\,\,(4 - 1)}}{2}\,\, = \,\,6\)

શકય સ્થાનતર \({\text{4}} \to {\text{ 3, 4 }} \to {\text{2, 4}} \to {\text{ 1, 3 }} \to {\text{2, 3 }} \to {\text{1, 2}} \to {\text{ 1}}\)