1 gm of radium is reduced by 2.1 mg is 5 years by alpha decay. Calculated the half life period 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
0.9979 = 1.0000e^k*5
ln0.9979 = e^5k
k = [0.9979]/5 =- 4.2044*10^-4
so
A = Aoe^-4.2044*10^-4*t
and we need t for A = Ao/2 ( ie half life)
Ao/2 = Aoe^-4.2044*10^-4*t
0.5 = e^-4.2044*10^-4*t
ln0.5 = -4.2044*10^-4*t
[ln0.5]/-4.2044*10^-4 = t
1648.6 years = t = answ
A = Aoe^kt
A = amount at time t
Ao = amount at t = 0
t = time
k = a constant
we are given
0.9979 = 1.0000e^k*5
ln0.9979 = e^5k
k = [0.9979]/5 =- 4.2044*10^-4
so
A = Aoe^-4.2044*10^-4*t
and we need t for A = Ao/2 ( ie half life)
Ao/2 = Aoe^-4.2044*10^-4*t
0.5 = e^-4.2044*10^-4*t
ln0.5 = -4.2044*10^-4*t
[ln0.5]/-4.2044*10^-4 = t
1648.6 years = t = answ
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