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------------------------------------------------ What is the wavelength of the Lyman series transition that starts at $ n = 4 $?

A) $ 9.73 \times 10^{-8} $ nm
B) $ 91.2 $ nm
C) $ 97.3 $ nm
D) $ 102.7 $ nm

Question

High School

Answer :

AryaneBliss AryaneBliss · Answer 1 · 2025-03-20T03:48:06-04:00

The wavelength of the Lyman series transition that starts at n=4 is approximately 97.3 nm. Option C) is correct.

The wavelength of the Lyman series transition that starts at n=4 can be calculated using the formula:

λ = R(1/n₁² - 1/n₂²)

Where R is the Rydberg constant, which is approximately 1.097 × 10^7 m⁻¹, and n₁ and n₂ are the initial and final energy levels, respectively.

In this case, the Lyman series starts at n=1 and the transition starts at n=4. Plugging in the values, we get:

λ = (1.097 × 10^7 m⁻¹)(1/4² - 1/1²)

Simplifying the expression gives us:

λ ≈ 97.3 nm

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