Energy splitting of the magnetic sub levels

In summary, to calculate the energy splitting of the magnetic sub levels in a 3S1 term, we use the formula ΔE = gSμBΔB, where g=1, S=1, μB=9.274×10^-24 J/T, and ΔB=1.5 T. This results in an energy splitting of 1.391×10^-23 J.
  • #1
vst98
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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=-gsμb*S/hbar

But I don't know how to calculate the splitting in energy from this.
 
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  • #2


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.
 

FAQ: Energy splitting of the magnetic sub levels

What is energy splitting of magnetic sub levels?

The energy splitting of magnetic sub levels refers to the phenomenon in which the energy levels of an atom or molecule split into distinct levels when placed in a magnetic field. This splitting is caused by the interaction between the magnetic field and the intrinsic magnetic moment of the atom or molecule.

What factors affect the energy splitting of magnetic sub levels?

The energy splitting of magnetic sub levels is affected by the strength of the magnetic field, the orientation of the magnetic field relative to the atom or molecule, and the magnitude of the intrinsic magnetic moment of the atom or molecule.

How is the energy splitting of magnetic sub levels measured?

The energy splitting of magnetic sub levels is typically measured using spectroscopic techniques, such as electron paramagnetic resonance (EPR) spectroscopy or nuclear magnetic resonance (NMR) spectroscopy. These techniques involve applying a magnetic field and measuring the energy absorbed or emitted by the atom or molecule.

What is the significance of energy splitting of magnetic sub levels?

The energy splitting of magnetic sub levels is important in understanding the electronic and magnetic properties of atoms and molecules. It can provide information about the atomic or molecular structure, as well as the strength of the magnetic interaction within a system.

How does energy splitting of magnetic sub levels impact everyday life?

The energy splitting of magnetic sub levels is not directly relevant to everyday life, but it has important applications in fields such as materials science, chemistry, and medicine. It is used to study the electronic and magnetic properties of materials, as well as to help design new materials with specific properties. In medicine, it is used in techniques such as MRI to image the internal structures of the body.

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