The half-life for the radioactive decay of U−238 is 4.5 billion years and is independent of initial concentration.
1.How long will it take for 10% of the U−238 atoms in a sample of U−238 to decay?
2.If a sample of U−238 initially contained 1.9×1018 atoms when the universe was formed 13.8 billion years ago, how many U−238 atoms will it contain today?
1. half life time(t1/2) = 4.5*10^9 years
K1 = 0.693/T1/2
= 0.693/(4.5*10^9)
= 1.54*10^-10 y-1
k = (1/t)ln(a0/a)
a0 = initial concentration = 100%
a = concentration remains after time t years = 90%
1.54*10^-10 = (1/t)ln(100/90)
t = 6.84*10^8 years
2.
k = (1/t)ln(a0/a)
a0 = initial concentration = 1.9*10^18 atoms
a = concentration remains after time t years = x
t = 13.8 billion = 13.8*10^9 years
1.54*10^-10 = (1/(13.8*10^9))ln((1.9*10^18)/x)
x = 2.27*10^17 atoms
U−238 atoms contain today = 2.27*10^7 atoms
The half-life for the radioactive decay of U−238 is 4.5 billion years and is independent of...
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