Question

What is the wavelength in nanometers of the first line in the Paschen series?

(A) 1876 nm

(B) 1282 nm

(C) 276 nm

(D) 1096 nm​

Answer 1

ANSWER↓

Wavelength of the first line of Paschen series is `- (R = 109700 cm^-1`).

Answer 2

The wavelength of the first line of the Paschen series is 1876 nm, hence option (A) is correct.

We have to find the wavelength in nanometres of the first line in the Paschen series.

Electron is transferred from n₁ = 3 to n₂ = 4 vice-versa for the first line of Paschen series.

Now using Rydberg's equation to find wavelength of transiting electron.

$\frac{1}{\lambda}=RZ^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

R = 109700 cm¯¹ , Z = 1

∴ 1/λ = 109700 × 1² × (1/3² - 1/4²)

⇒1/λ = 109700 × (1/9 - 1/16)

⇒1/λ = 109700 × 7/(9 × 16)

⇒λ = (144)/(109700 × 7) ≈ 0.0001876 cm

We know,

$1nm = {10}^{7} cm$

∴ λ = 1876 nm

Therefore the wavelength of the first line of the Paschen series is 1876 nm.

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