Question

The first member of the Paschen series in hydrogen spectrum is of wavelength $18,800\stackrel{\circ }{A}$. The short wavelength limit of Paschen series is

• A. $1215\stackrel{\circ }{A}$
• B. $6560\stackrel{\circ }{A}$
• C. $8225\stackrel{\circ }{A}$
• D. $12850\stackrel{\circ }{A}$

Answer 1

The correct option is C $8225\stackrel{\circ }{A}$

First member of Paschen series mean it's ${\lambda }_{max}=\frac{144}{7R}$
Short wavelength of Paschen series means ${\lambda }_{min}=\frac{9}{R}$
Hence $\frac{{\lambda }_{max}}{{\lambda }_{min}}=\frac{16}{7}\Rightarrow {\lambda }_{min}=\frac{7}{16}\times {\lambda }_{max}=\frac{7}{16}\times 18,800=8225\stackrel{\circ }{A}$