Answer:
The half life of the material approximately 7years
Explanation:
Half life is defined as the time taken by a radioactive material to decay to half of its original substance.
Half life t1/2 = ln2/λ
λ is the decay constant.
To get the decay constant , we will use the relationship
N = Noe^-λt
No is the initial value of the substance
N is the final value of the substance after decay
t is the time taken by the substance to decay.
From the formula
N/No = e^-λt ... (1)
If radioactive nuclei decreases to one-sixteenth the number present initially, this means N = 1/16No
N/No = 1/16
t = 29days
Substituting this values into equation 1 we have:
1/16 = e^-29λ
Taking the ln of both sides
ln(1/16) = lne^-29λ
ln(1/16) = -29λ
λ = ln(1/16)/-29
λ = ln0.0625/-29
λ = -2.77/-29
λ = 0.0955
Substituting λ = 0.0955 into the half life formula, we have;
t1/2 = ln2/0.0955
t1/2 = 7.26days
The half life of the materia is 7.26years
Answer:
In 29 days, the number of radioactive nuclei decreases to one-sixteenth the number present initially. What is the half-life (in days) of the material
Explanation:
The radioactive decay law says
N(t) = No•2^(-t/t½)
Then,
In 29 days
t = 29
The radioactive element has decreased to one-sixteenth of it's original
Then, N(t) / No = 1/16i
Now,
N(t) = No•2^(-t/t½)
N(t) / No = 2^(-t/t½)
1/16 = 2^(-29/t½)
Take In base 2 of both sides
In(1/16) = In•2^(-29/t½)
In(2^-4) = -29/t½
-4In(2) = -29 / t½
Since the ln is in base 2 then, In(2) =1
-4 = -29 / t½
Therefore
t½ = -29 / -4
t½ = 7.25 days
t½ ≈ 7 days
So, the half life of the radioactive element is approximately 7 days
