Radioactive Decay and Half-Life of Cobalt-60

The video tutorial explores the concept of radioactive half-life using cobalt-60 as an example. It poses two main questions: calculating the decay constant and determining the fraction of cobalt-60 nuclei remaining after 15 years. The tutorial explains the mathematical expressions needed to solve these problems, including the use of the natural logarithm and exponential decay formulas. By the end, viewers learn how to calculate the decay constant and the remaining fraction of radioactive material over time.

What is the half-life of Cobalt-60?

• 5.27 years

• 10.54 years

• 2.63 years

• 7.5 years

What is the decay constant formula in terms of half-life?

• Half-life = ln(2) / decay constant

• Decay constant = ln(2) / half-life

• Decay constant = half-life / ln(2)

• Half-life = decay constant / ln(2)

What is the value of the natural log of 2 used in decay calculations?

• 0.5

• 0.693

• 1.0

• 1.386

Which expression is used to calculate the remaining fraction of nuclei?

• nt = n0 / lambda t

• nt = n0 * lambda t

• nt = n0 + lambda t

• nt = n0 e^(-lambda t)

What does 'n0' represent in the expression nt = n0 e^(-lambda t)?

• Decay constant

• Time elapsed

• Final number of nuclei

• Initial number of nuclei

How do you calculate the fraction of nuclei remaining after a certain time?

• t / lambda

• lambda / t

• n0 / nt

• nt / n0

What is the decay constant of Cobalt-60?

• 0.132 years^-1

• 0.693 years^-1

• 1.0 years^-1

• 0.5 years^-1

After 15 years, what percentage of Cobalt-60 nuclei remains?

• 25%

• 50%

• 75%

• 13.8%

How many half-lives approximately correspond to 15 years for Cobalt-60?

• Four half-lives

• Two half-lives

• Exactly three half-lives

• Just under three half-lives

What is the significance of the decay constant in radioactive decay?

• It is the final amount of substance

• It determines the rate of decay

• It measures the initial amount of substance

• It is the time taken for complete decay