SME
Physical Chemistry II: Quantum & Spectroscopy · Problem type
The g-factor from an EPR line
Use this for “A radical absorbs 9.400 GHz microwaves at a field of 0.3355 T. Find its g-factor.”
Chart
This is an example. Type your own values to start a new problem.
h
ν (GHz)
=
g
μB
B (T)
Formulas
g
=
6.626 ×
10
-34
×
ν
×
10
9
9.274 ×
10
-24
×
B
2.0022
=
6.626 ×
10
-34
×
9.5 ×
10
9
9.274 ×
10
-24
× 0.339
Assumptions
•
One unpaired electron: in a field B its two spin levels sit at +½gμBB and −½gμBB.
•
Resonance comes when the microwave photon matches the gap: hν = gμBB.
•
h = 6.626 × 10⁻³⁴ J·s and μB = 9.274 × 10⁻²⁴ J/T; the graph gives the levels as E ÷ h in GHz.
Step-by-step
WE KNOW
ν = 9.5 GHz, B = 0.339 T
FIND
g-factor (g)
Step 1 · Find g-factor (g)
Use g = 6.626 × 10⁻³⁴ × ν × 10⁹ ÷ (9.274 × 10⁻²⁴ × B)
The
photon’s
energy
hν,
with
ν
in
hertz,
divided
by
μB
times
the
field.
g
=
6.626 ×
10
-34
×
9.5 ×
10
9
9.274 ×
10
-24
× 0.339
g
=
(6.626
×
10
-34
)
×
9.5 ×
10
9
3.1439 ×
10
-24
g
=
6.2947 ×
10
-24
3.1439 ×
10
-24
g
=
2.0022
→
g
is
close
to
the
free
electron’s
2.0023:
an
organic
radical,
its
unpaired
electron
hardly
feels
orbital
motion.
Check
Put the numbers back in. Both sides should match.
2.0022
=
6.626 ×
10
-34
×
9.5 ×
10
9
9.274 ×
10
-24
× 0.339
✓
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