How Long Does It Take for Nickel-63 to Decay?
Question:
If a sample of nickel-63 decays until 6.25% of the original sample remains, how much time has passed?
A. 6.25 years
B. 100 years
C. 400 years
D. 1600 years
Answer:
The correct answer is C. 400 years.
Radioactive decay is a process that occurs in unstable isotopes, such as nickel-63. The half-life of nickel-63 is 100 years, which means it takes 100 years for half of the original sample to decay.
In this scenario, when 6.25% of the original sample remains, we can use the formula for radioactive decay to calculate the time that has passed. The equation that describes the decay is:
m(t) = m0 (1/2)t/t1/2
Where:
m(t) is the amount of sample left at time t
m0 is the initial amount of the sample
t1/2 is the half-life of the isotope
Given that 6.25% of the original sample remains, we can set up the equation:
6.25% = (1/2)t/t1/2
Solving for t, we find that t = 4 x t1/2 = 4 x 100 = 400 years. Therefore, it takes 400 years for nickel-63 to decay until 6.25% of the original sample remains.