Practice Problem: Radioactive Half-Life

Professor Dave explains the concept of radioactive half-life using Cobalt-60, which decays to Nickel-60 with a half-life of 5.27 years. The video covers calculating the decay constant using the natural log of 2 and determining the fraction of Cobalt-60 nuclei remaining after 15 years. The decay constant is found to be 0.132 years^-1, and the fraction of nuclei remaining after 15 years is 13.8%.

What is the primary element discussed in the radioactive decay problem?

• Carbon-14

• Cobalt-60

• Uranium-238

• Nickel-60

Which mathematical expression is used to calculate the decay constant?

• Half-life = ln(2) / decay constant

• Decay constant = ln(2) / half-life

• Half-life = decay constant / ln(2)

• Decay constant = half-life / ln(2)

What is the value of the decay constant for Cobalt-60?

• 1.98 years^-1

• 5.27 years^-1

• 0.132 years^-1

• 0.693 years^-1

Which formula is used to determine the fraction of nuclei remaining after a certain time?

• N0 = Nt * e^(lambda * t)

• N0 = Nt * e^(-lambda * t)

• Nt = N0 * e^(lambda * t)

• Nt = N0 * e^(-lambda * t)

What percentage of Cobalt-60 nuclei remains after 15 years?

• 0%

• 25%

• 50%

• 13.8%