Question

Calculate the wavelength of the second line of lyman series in hydrogen spectra (given RH =1an.09737 c /M)

Answer 1

R value is constant= 1.08×10power7metreinverse
1/wave length=R[1/n1square_1/n2 square]

n1=1,n2= 3

1/wave length=1.08×10power7 ×8÷9

wave length =10.4×10power_8cm

Answer 2

Given:

Rydberg constant - R = 1.097 × 10⁷ m⁻¹

To Find:

The wavelength of the second line of the Lyman series - λ =?

Solution:

Concept and Formula used:

• The Lyman series is the ultraviolet emission line of the hydrogen atom due to the transition of an electron from n ≥ 2 to n = 1
• Here, the transition is from n = 3 to n = 1 , Therefore, n₁ = 1  and n₂ = 3
• Formula: 1/λ = R[ 1/n₁² - 1/n₂²]

Applying the above formula to calculate the wavelength of the second line of the Lyman series in hydrogen spectra:-

1/λ = R[ 1/n₁² - 1/n₂²]

1/λ = R [1/1² - 1/3²]

1/λ = R[1 - 1/9]

1/λ = R[$\frac{9 - 1}{9}$]

1/λ = R8/9

Substituting the value of R:

1/λ = 1.907 × 10⁷ × 8/9

λ = $\frac{9 * 10^{-7} }{8 * 1.907}$

λ = 1.125/1.907 × 10⁻⁷

λ = 0.59 × 10⁻⁷ m

Hence, the wavelength of the second line of the Lyman series in hydrogen spectra = 0.59 × 10⁻⁷ m