Energy splitting of the magnetic sub levels

[vst98]

Homework Statement

Calculate the energy splitting of the magnetic sub levels of a ³S₁ term in a magnetic field of 1.5 T.

The Attempt at a Solution

From the term symbol ³S₁ I can conclude:
S -> L=0
subscript 1 -> J=1
superscript 3 -> 3=2S+1 -> S=1

Therefore I have two electrons with spin +1/2 so the corresponding electron configuration is
1s¹2s¹

I know that Electron in an magnetic filed has potential energy:
E=μ*B , where μ=-g_sμ_b*S/hbar

But I don't know how to calculate the splitting in energy from this.

 

[mark726]

Hello, great question! To calculate the energy splitting of the magnetic sub levels in a 3S1 term, we can use the following formula:

ΔE = gSμBΔB

Where:
ΔE = energy splitting
g = Landé g-factor (1 for S orbital)
S = total spin quantum number (1 for S orbital)
μB = Bohr magneton
ΔB = change in magnetic field strength (1.5 T in this case)

Plugging in the values, we get:

ΔE = (1)(1)(9.274×10^-24 J/T)(1.5 T)
ΔE = 1.391×10^-23 J

This is the energy splitting between the two magnetic sub levels in a 3S1 term in a magnetic field of 1.5 T. I hope this helps! Let me know if you have any further questions.