We can solve this problem by using the half-life formula:
N(t) = N₀ * (1/2)^(t/T)
where:
N(t) is the remaining percentage of radioactive atoms after time t
N₀ is the initial percentage of radioactive atoms (100% in this case)
t is the time that has passed
T is the half-life of the radioactive element
In this problem, we know that N(t) is 12.5% and T is 800 years. We want to find t.
12.5% = 100% * (1/2)^(t/800)
Divide both sides of the equation by 100%:
0.125 = (1/2)^(t/800)
Take the logarithm (base 2) of both sides to isolate t/800:
log₂(0.125) = t/800
Simplify the left side of the equation:
log₂(1/8) = t/800
Rewrite 1/8 as 2^(-3):
-3 = t/800
Multiply both sides of the equation by 800:
-3 * 800 = t
t = -2400
Since time cannot be negative, we discard the negative solution, so t = 2400 years.
Therefore, the object is 2400 years old.
The correct answer is not listed in the options provided.
The half-life of a certain radioactive element is 800 years. How old is an object if only 12.5% of the radioactive atoms in it remain?
A. 3200 years
B. 1600 years
C. 6400 years
1 answer
1 answer