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/t_1/2

Where:

m(t) is the amount of sample left at time t

m₀ is the initial amount of the sample

t_1/2 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/t_1/2

Solving for t, we find that t = 4 x t_1/2 = 4 x 100 = 400 years. Therefore, it takes 400 years for nickel-63 to decay until 6.25% of the original sample remains.