The longest wavelength associated with Paschen series is : (Given $\mathrm{R}_{\mathrm{H}}=1.097 \times 10^{7} \mathrm{SI}$ unit)

(D) $1.876 \times 10^{-6} \mathrm{~m}$

(A) $1.094 \times 10^{-6} \mathrm{~m}$

(B) $3.646 \times 10^{-6} \mathrm{~m}$

(C) $2.973 \times 10^{-6} \mathrm{~m}$

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Modern Physics

The longest wavelength associated with Paschen series is : (Given

R_{H} = 1.097 \times 1 0^{7} SI

unit)

(A) $1.094 \times 1 0^{- 6} m$
(B) $3.646 \times 1 0^{- 6} m$
(C) $2.973 \times 1 0^{- 6} m$
(D) $1.876 \times 1 0^{- 6} m$ ✓ Correct

Answer: (D)

Solution

The longest wavelength in the Paschen series comes from the smallest energy gap, the transition from

n = 4

n = 3

. Using

\frac{1}{λ} = R_{H} (\frac{1}{3 ^{2}} - \frac{1}{4 ^{2}}) = 1.097 \times 1 0^{7} \times \frac{7}{144} = 5.33 \times 1 0^{5} m^{- 1}

, so

λ = 1.876 \times 1 0^{- 6} m

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Single correct option

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