Half-life

What is the half-life of a radioactive element?

The half-life (t_{1/2}) of a radioactive element is the time taken for half of the radioactive nuclei in a given sample to decay.

What does the half-life indicate about a radioactive isotope?

It indicates the rate of radioactive decay. A shorter half-life means a faster decay rate, and a longer half-life means a slower decay rate.

Is the half-life of a radioactive element affected by external factors?

No, the half-life of a radioactive element is a characteristic constant for a specific isotope and is independent of external factors such as temperature, pressure, or chemical environment.

How is the fraction of remaining radioactive material related to the number of half-lives?

After n half-lives, the fraction of the original radioactive material remaining is (1/2)^n.

What is the half-life of a radioactive element?

The half-life (t_{1/2}) of a radioactive element is the time taken for half of the radioactive nuclei in a given sample to decay.

What does the half-life indicate about a radioactive isotope?

It indicates the rate of radioactive decay. A shorter half-life means a faster decay rate, and a longer half-life means a slower decay rate.

Is the half-life of a radioactive element affected by external factors?

No, the half-life of a radioactive element is a characteristic constant for a specific isotope and is independent of external factors such as temperature, pressure, or chemical environment.

How is the fraction of remaining radioactive material related to the number of half-lives?

After n half-lives, the fraction of the original radioactive material remaining is (1/2)^n.

What is the formula for calculating the amount of radioactive material remaining after a certain time?

The formula is N(t) = N0 (1/2)^{t/t{1/2}}, where:

• N(t): amount of radioactive material remaining after time t
• N_0: initial amount of radioactive material
• t: total time elapsed
• t_{1/2}: half-life of the radioactive element

Alternatively, it can be expressed as N(t) = N0 / 2^n, where n is the number of half-lives elapsed (n = t/t{1/2}).

If a sample initially has 100g of a radioactive isotope with a half-life of 5 years, how much will remain after 15 years?

1. Calculate the number of half-lives:
   n = \text{total time} / \text{half-life} = 15 \text{ years} / 5 \text{ years} = 3

2. Calculate the remaining fraction:
   (1/2)^n = (1/2)^3 = 1/8

3. Calculate the remaining amount:
   \text{Remaining amount} = \text{Initial amount} \times \text{Remaining fraction} = 100 \text{g} \times (1/8) = 12.5 \text{g}

Explain how to calculate the half-life (t{1/2}) if you know the initial amount (N0), the final amount (N(t)), and the total time elapsed (t).

1. Determine the number of half-lives (n):
   First, find the fraction remaining: N(t)/N0. Then, find n such that (1/2)^n = N(t)/N0. This often involves using logarithms: n = \log{1/2}(N(t)/N0).

2. Calculate the half-life:
   t_{1/2} = t/n

A sample decays from 800 Bq to 100 Bq in 60 minutes. What is its half-life?

1. Determine the fraction remaining:
   \text{Fraction} = \text{Final amount} / \text{Initial amount} = 100 \text{ Bq} / 800 \text{ Bq} = 1/8

2. Determine the number of half-lives (n):
   Since (1/2)^n = 1/8, we know that n = 3 (because 1/2 \times 1/2 \times 1/2 = 1/8).

3. Calculate the half-life:
   t_{1/2} = \text{Total time} / \text{Number of half-lives} = 60 \text{ minutes} / 3 = 20 \text{ minutes}