1g of radium is reduce by 2mg in 5 years by alpha decay. Calculate the half life time of radium
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Equation for exponential growth/decay:
A = Aoe^kt
A = amount at time t
Ao = amount at t = 0
t = time
k = a constant
we are given
0.998 = 1.0000e^k*5
ln(0.998) = e^5k
k = [ln(0.998)]/5 = -4 x 10^-4
so
A = Aoe^-4 x 10^-4t
and we need t for A = Ao/2 ( ie half life)
Ao/2 = Aoe^-4 x 10^-4t
0.5 = e^-4 x 10^-4t
ln0.5 = -4 x 10^-4t
[ln0.5]/-4 x 10^-4 = t
1732.86 years = t = answer
i hope it will help you
regards
A = Aoe^kt
A = amount at time t
Ao = amount at t = 0
t = time
k = a constant
we are given
0.998 = 1.0000e^k*5
ln(0.998) = e^5k
k = [ln(0.998)]/5 = -4 x 10^-4
so
A = Aoe^-4 x 10^-4t
and we need t for A = Ao/2 ( ie half life)
Ao/2 = Aoe^-4 x 10^-4t
0.5 = e^-4 x 10^-4t
ln0.5 = -4 x 10^-4t
[ln0.5]/-4 x 10^-4 = t
1732.86 years = t = answer
i hope it will help you
regards
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