Answer :
Final answer:
The wavelength of the second line in the Lyman series for a hydrogen atom is calculated using the Rydberg formula and found to be 102.5 nm. Option B.
Explanation:
The question is asking to calculate the wavelength of the 2nd line in the Lyman series for a hydrogen atom. The Rydberg formula is used to find the wavelength of lines in the emission spectrum of hydrogen:
1/λ = R × (1/n1² - 1/n2²), where λ is the wavelength, R is the Rydberg constant, n1 is the lower energy level, and n2 is the higher energy level. In the Lyman series, n1 is always 1, as electrons are falling back to the ground state. So for the 2nd line of Lyman series (Lyman beta), the electron falls from n2 = 3 to n1 = 1.
Using the given Rydberg constant value R = 1.097 × 10⁷ cm⁻¹ and the formula:
1/λ = (1.097 × 10⁷) × (1/1² - 1/3²)
1/λ = (1.097 × 10⁷) × (1 - 1/9)
1/λ = (1.097 × 10⁷) × (8/9)
λ = 9 / (8 × 1.097 × 10⁷) cm = 1.02 × 10⁻² cm = 102.5 nm
Therefore, the wavelength of the 2nd line in the Lyman series for the hydrogen atom is 102.5 nm.
