A chemist observed an unknown Balmer Series decay through an emission of 410 nm. Using the experimental wavelength, determine the energy levels transition involved in the emitted wavelength.

Option D is correct.

n = 6 to n = 2

Explanation:

Like all waves emitted from the movement of electrons from one energy level to another, the wavelength (λ) is given by the equation involving Rydberg's constant

(1/λ) = Rₕ [(1/n₂²) - (1/n₁²)]

where Rₕ = 10973731.57 m⁻¹ = (1.0974 × 10⁷) m⁻¹

n₂ = principal quantum number corresponding to the final energy level of the electron = 2 (For Balmer Series)

n₁ = principal quantum number corresponding to the final energy level of the electron = ?

λ = 410 nm = (410 × 10⁻⁹) m

(1/λ) = (2.439 × 10⁶) m⁻¹

2.439 × 10⁶ = (1.0974 × 10⁷) [(1/2²) - (1/n₁²)]

0.25 - (1/n₁²) = (2.439 × 10⁶) ÷ (1.0974 × 10⁷) = 0.2222602562

(1/n₁²) = 0.25 - 0.2222602562 = 0.0277397438

n₁² = (1/0.0277397438) = 36.05

n₁ = 6

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