the isotope caesium-137 has a half life of 30 years how long will it take for the amount of this isotope in a sample of caesium to decay to 1/16th of its origional amount. thanks
amountremaining=oriinalamount(1/2)^time/timehalflife.
1/16= (1/2)^t/30
(1/2)^4= (1/2)^t/30
so t/30= 4
solve for t in years.
Another, but longer way, of solving the problem follows:
k=0.693/t1/2
solve for k. THEN,
ln(No/N)=kt
where No = original # atoms = 16
N = # atoms at some future time = 1
k is from above.
solve for t.
You should get the same answer either way.
To find the time it takes for the amount of caesium-137 to decay to 1/16th of its original amount, we can use the equation:
amount remaining = original amount * (1/2)^(time / half-life)
We are given that the half-life of caesium-137 is 30 years. Let's denote the original amount as N_o, and the amount remaining as N.
We want to find the value of time when N equals 1/16 of N_o. Substituting these values into the equation:
1/16 = N_o * (1/2)^(time / 30)
Simplifying the equation:
(1/2)^4 = (1/2)^(time / 30)
Since the bases are the same, we can equate the exponents:
4 = time / 30
To find the value of time, we can solve for it by multiplying both sides of the equation by 30:
4 * 30 = time
120 = time
Therefore, it will take 120 years for the amount of caesium-137 in a sample to decay to 1/16th of its original amount.