Polonium-209, an a emitter, has a half-life of 102 years. How many alpha particles are emitted in 1.0 s from a 1.0 ng sample of 209Po?

Verified step by step guidance

1. Step 1: The first step is to calculate the number of atoms in the 1.0 ng sample of Polonium-209. This can be done using Avogadro's number (6.022 x 10^23 atoms/mol) and the molar mass of Polonium-209 (209 g/mol). Remember to convert the mass of the sample from nanograms to grams.
2. Step 2: Next, calculate the decay constant (λ) for Polonium-209. The decay constant can be calculated using the formula λ = ln(2) / t_half, where t_half is the half-life of the isotope. In this case, the half-life is given as 102 years, but you need to convert this to seconds because the problem asks for the number of alpha particles emitted in 1.0 s.
3. Step 3: Now, calculate the number of decays per second (also known as the activity of the sample) using the formula A = λN, where A is the activity, λ is the decay constant, and N is the number of atoms. This will give you the number of atoms that decay each second.
4. Step 4: Since each decay of Polonium-209 produces one alpha particle, the number of alpha particles produced per second is equal to the number of decays per second.
5. Step 5: Therefore, the number of alpha particles emitted in 1.0 s from a 1.0 ng sample of 209Po is equal to the activity of the sample.

Key Concepts

Half-life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. For Polonium-209, with a half-life of 102 years, this means that after 102 years, only half of the original amount of 209Po will remain. Understanding half-life is crucial for calculating the decay of radioactive substances over time.

Radioactive decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation, such as alpha particles. In the case of Polonium-209, it undergoes alpha decay, releasing alpha particles as it transforms into a different element. This concept is essential for determining the number of particles emitted over a specific time frame.

Activity and decay constant

The activity of a radioactive sample is the rate at which decay events occur, typically measured in decays per second. It is related to the decay constant, which quantifies the probability of decay per unit time. For Polonium-209, knowing the activity allows us to calculate how many alpha particles are emitted from a given mass over a specified duration, such as 1.0 second.