Emission transiti

Given:

Wavelength, λ = 1285 nm

Frequency, v = 3.29 × 10¹⁵ [1/3² – 1/n²] (Hz)

Speed of Light = [Frequency] × [Wavelength]

We know speed of light = 3×10⁸ m/s

Frequency, v = [3×10⁸] / [1285 × 10^-9]

v = 2.3346×10¹⁴ Hz

3.29 × 10¹⁵ [1/3² – 1/n²] = 2.3346×10¹⁴

[1/3² – 1/n²] = [2.3346×10¹⁴] / [3.29 × 10¹⁵]

[1/3² – 1/n²] = 0.07427

[1/9] – 0.07427 = 1/n²

1/n² = 0.04

1/n² = 1 / 25

n² = 25

n = 5

The value of n is 5.