# 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) = m _{0} (1/2)^{t/t1/2}**

Where:

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

m_{0} 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/t1/2}

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.