Emission transitions in the Panchen series end at orbit n = 3 and start from orbit n and can be represented as v = 3.29 × 10 15 (Hz) [1/3 2 – 1/n 2 ] Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.

Question

Philoid · Accepted Answer

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.

Emission transitions in the Panchen series end at orbit n = 3 and start from orbit n and can be represented as v = 3.29 × 1015 (Hz) [1/32 – 1/n2]Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.

Emission transitions in the Panchen series end at orbit n = 3 and start from orbit n and can be represented as v = 3.29 × 10¹⁵ (Hz) [1/3² – 1/n²]
Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.