SME
University Physics III: Waves, Optics & Modern · Problem type
A force’s range from its carrier’s mass
Use this for “The pion has a rest energy of 139.6 MeV. Estimate the range of the force it carries.”
This is an example. Type your own values to start a new problem.
R (fm)
=
197.3
MeV·fm
mc² (MeV)
Δt
Time the carrier lasts
worked out (not typed) · s
Formulas
R
=
197.3
mc²
1.413
=
197.3
139.6
Δt
=
6.583 ×
10
-22
mc²
4.7156 ×
10
-24
=
6.583 ×
10
-22
139.6
Assumptions
•
The energy–time uncertainty lets the carrier’s rest energy mc² be borrowed for about Δt ≈ ħ ÷ mc², with ħ = 6.583 × 10⁻²² MeV·s.
•
Moving at nearly light speed, the carrier gets about R ≈ cΔt = ħc ÷ mc² before it must vanish; ħc = 197.3 MeV·fm.
•
A massless carrier such as the photon has no such limit, so its force reaches infinitely far.
Step-by-step
WE KNOW
mc² = 139.6 MeV
FIND
range of the force (R), time the carrier lasts (Δt)
Step 1 · Find range of the force (R)
Use R = 197.3 ÷ mc²
The
carrier
covers
about
cΔt
=
ħc
mc²
;
with
ħc
=
197.3
MeV·fm
the
range
comes
out
in
fm.
R
=
197.3
139.6
R
=
1.413
fm
Step 2 · Find time the carrier lasts (Δt)
Use Δt = 6.583 × 10⁻²² ÷ mc²
Borrowing
the
energy
mc²
is
allowed
for
about
ħ
mc²
;
ħ
=
6.583 ×
10
-22
MeV·s.
Δt
=
6.583 ×
10
-22
139.6
Δt
=
4.7156 ×
10
-24
s
Check
Put the numbers back in. Both sides should match.
1.413
=
197.3
139.6
✓
4.7156 ×
10
-24
=
6.583 ×
10
-22
139.6
✓
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