Light is emitted by hydrogen atoms in the visible range for a hydrogen atom. Its wavelength is 656 nm. What value of n is associated with the light? (R_H = 1.097 × 10⁷ m−¹) A) 5 B) 2 C) 4 D) 3 E) 6

Question

Quizplus · Accepted Answer

The wavelength of the emitted light is related to the energy difference between the levels of the hydrogen atom. Using the Rydberg formula, we can calculate the value of n for the emitted light:

1/λ = R(1/n₁² - 1/n₂²)

where λ is the wavelength of the light, R is the Rydberg constant (1.097 × 10^7 m^-1), and n₁ and n₂ are the initial and final energy levels of the electron.

In this case, the wavelength is given as 656 nm, which we convert to meters (656 × 10^-9 m). The initial level is the ground state (n₁ = 1) and the final level is the first excited state (n₂ = 2). Substituting these values into the equation and solving for n₂:

1/656 × 10^-9 = 1.097 × 10^7 (1/1² - 1/n₂²)

1/n₂² = 1 - (656 × 10^-9)(1.097 × 10^7)

n₂ = 3

Therefore, the answer is choice D.

Light Is Emitted by Hydrogen Atoms in the Visible Range