The wavelength (in cm) of second line in the Lyman series of hydrogen atomic spectrum is (Rydberg constant = R cm-1)

Question

The wavelength (in cm) of second line in the Lyman series of hydrogen atomic spectrum is (Rydberg constant = R cm-1) (A) ((8R/9)) (B) ((9/8R)) (C) ((4/3R)) (D) ((3R/4))

Tardigrade Admin · Accepted Answer

vecv=(1/λ)=R[(1/n21)-(1/n22)] For second line in lyman series n2 = 3 ∴ (1/λ)=R[(1/12)-(1/32)]=R[(1/1)-(1/9)]=(8 R/9) ∴ λ=(9/8 R)

Q. The wavelength (in cm) of second line in the Lyman series of hydrogen atomic spectrum is (Rydberg constant = R cm^-1)

$(\frac{8 R}{9})$

$(\frac{9}{8 R})$

$(\frac{4}{3 R})$

$(\frac{3 R}{4})$

$v = \frac{1}{λ} = R [\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}]$
For second line in lyman series
n₂ = 3
$∴ \frac{1}{λ} = R [\frac{1}{1 ^{2}} - \frac{1}{3 ^{2}}] = R [\frac{1}{1} - \frac{1}{9}] = \frac{8 R}{9}$
$∴ λ = \frac{9}{8 R}$

Q. The wavelength (in cm) of second line in the Lyman series of hydrogen atomic spectrum is (Rydberg constant = R cm-1)

(98R​)

(8R9​)

(3R4​)

(43R​)