A sample of tritium-3 decayed to 94.5\% of its original

Paganellash

Paganellash

Answered question

2021-11-23

A sample of tritium-3 decayed to 94.5% of its original amount after a year. What is the half-life of tritium-3?

Answer & Explanation

Steven Arredondo

Steven Arredondo

Beginner2021-11-24Added 18 answers

Step 1
A=A0ekt
t is in years
After 1 year t=1 and A=0.945A0
Substitute to get
1) 0.945=ek
Let half life be x. Then A=0.5A0
Substitute to get 0.5=ekx
0.5=(ek)x
Substitute 0.945ek Using eqn(1)
0.5=(0.945)x
Take ln on both sides to get
ln(0.5)=xln(0.945)
x=ln(0.5)ln(0.945)=12.25
Half life is 12.25 years
Elizabeth Witte

Elizabeth Witte

Beginner2021-11-25Added 24 answers

Step 1
Notice,
P(t)=P0ekt
Where, growth rate
k=λ=ln2t12
Since, the amount after time t=1 year decays to P(t)=94.5% of initial value P0 hence substituting the corresponding values in the formula as follows
94.5100P0=P0eλ×1
eλ=0.945
λ=ln(0.945)
Hence the half life of tritium-3 is given
t12=ln2ln(0.945)=12.25 years

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