Question

Determine the wavelength of a line that splits into three lines in the presence of an external magnetic field of strength 4.50 T if the distance between the adjacent lines is 0.0361 nm. (a) 565 nm (b) 172 nm (c) 330 nm (d) 415 nm​

Answer 1

Concept:

We need to utilize the relation, hcΔd/λ² = μ_BB for the determination of wavelength.

Given:

Magnetic field = 4.5 T

distance between adjacent lines, Δd = 0.0361nm

Find:

We need to determine the wavelength, λ of a line that splits into three lines in the presence of an external magnetic field.

Solution:

We have the formula,

ΔE = μ_BB  

We know, hΔv = hcΔλ/λ2 which in turn is equal to μ_BB

Therefore,

hcΔd/λ² = μ_BB

hcΔd /μ_BB  = λ²

λ² = hcΔd /μ_BB

λ² = (6.63 × 10^-34) × 3×10^8) × 0.0361 ×10^-9 / (9.17×10^-24) × 4.50

λ² = 0.7180 × 10^-35 / 41.265 × 10^-24

λ² = 0.01739 × 10^-11

λ = 415 nm

Thus, the wavelength of a line that splits into three lines in the presence of an external magnetic field of strength is 415nm.

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