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41. If
N
is the number of undecayed nuclei present at time
t
,then
dN
dt
=
R
−
λN
where
R
is the rate of production by the cyclotron and
λ
is the disintegration constant. The second
term gives the rate of decay. Rearrange the equation slightly and integrate:
Z
N
N
0
dN
R
−
λN
=
Z
t
0
dt
where
N
0
is the number of undecayed nuclei present at time
t
= 0. This yields
−
1
λ
ln
R
−
λN
R
−
λN
0
=
t.
We solve for
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 Fall '08
 SPRUNGER
 Physics, Light

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