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Physics 344
Foundations of 21
st
Century Physics:
Relativity, Quantum Mechanics and
heir Applications
Their Applications
Instructor:
Dr. Mark Haugan
Office:
PHYS 282
[email protected]
TA:
Dan Hartzler
Office:
PHYS 7
[email protected]
Grader:
Shuo Liu
Office:
PHYS 283
[email protected]
Office Hours: If you have questions, just email us to make an
ppointment.
e enjoy talking about physics!
appointment.
We enjoy talking about physics!
Notices: Locate your old copy of Matter & Interactions Volume II
Exam I average was
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View Full Document Particle Decays and Radioactivity
When a sample of unstable matter initially containing
N
0
active particles is
observed over a period of time its activity (average number of particle decays
per second) decreases exponentially with time. The rate at which the number
of particles in the sample changes over time is, therefore,
0
t
dN
e
dt
λ
−
⎛⎞
=
<
⎜⎟
⎝⎠
0
where
λ
, the decay constant, is a characteristic of the particular unstable
particle involved and is simply related to the particle’s halflife as we showed
last time.
This implies that the number of particles present in the sample at time
t
is
)
tt
t
t
N
d
t N
e d
t
′
−
′
+
=+
⎟
∫
( )
00
0
()
1
1
t
t
t
Nt
e
NN
e
t
′
−
−
′
−
∫∫
0
λλ
−
Since
( )
00
11
lim
( )
1
0
t
tt
dN
Nt
N
e
N
dt
λ
λλ
−
→∞
→∞
⎛⎞
=+
−
=
⎜⎟
⎝⎠
we conclude that
0
0
1
N
=−
o, we can express
N(t)
in the simpler form
So,
e ca e p ess
()
es pe o
( )
0
1
N N
e
Ne
−
−
−
=
N
d
N
e
N
t
−
−
⇒
=
Because the average rate at which unstable particles in a sample of matter
decay is proportional to the number of unstable particles in the sample, we
can say that the probability of any one of the unstable particles decaying
during a time interval
Δ
t
is
decay probability during
(number of decays during
)/
N t
ΔΔ
=
=
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View Full Document Quantum mechanics predicts such probabilities and only
such probabilities. It
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Garfinkel
 mechanics

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