Ncert Exercises & Solutions

12.3 What is the shortest wavelength present in the Paschen series of spectral lines?

Hint: Use the Rydberg's formula.

Step 1: Write an expression for the Rydberg's formula.
Rydberg's formula is given as,

\frac{h c}{λ} = 21.78 \times 10^{- 19} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]

where,
h=Planck's constant

= 6.62 \times 10^{- 34} J-sec

and c = speed of light =

3 \times 10^{8} m / s

Step 2: Find the value of n1 and n2 for shortest wavelength in Paschen series.
The shortest wavelength present in the Paschen series of the
spectral lines is given for values,

n_{1} = 3 a n d n_{2} = \infty .

Step 3: Find the shortest wavelength in Paschen series.

\begin{aligned} \frac{h c}{λ} & = 21.78 \times 10^{- 19} [\frac{1}{(3)^{2}} - \frac{1}{(\infty)^{2}}] \\ λ & = \frac{6.62 \times 10^{- 34} \times 3 \times 10^{8} \times 9}{21.78 \times 10^{- 19}} \\ = 8.181 \times 10^{- 7} m \\ = 818.1 nm \end{aligned}

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