Nitrogen-16 is formed in the cooling water flowing through a hot reactor core in a nuclear power plant. It is formed when oxygen captures a neutron and then emits a b par-ticle. Determine the activity of 50.0 mg of 16N in units of Bq and Ci.

Verified step by step guidance

1. Identify the decay process of Nitrogen-16 (16N). It decays by beta emission, and you need to know its half-life to proceed. The half-life of 16N is approximately 7.13 seconds.
2. Calculate the number of moles of 16N in 50.0 mg. Use the molar mass of 16N, which is approximately 16 g/mol. Number of moles = mass (g) / molar mass (g/mol).
3. Convert the number of moles of 16N to the number of atoms. Use Avogadro's number (approximately 6.022 x 10^23 atoms/mol). Number of atoms = moles x Avogadro's number.
4. Calculate the decay constant (\(\lambda\)) using the formula \(\lambda = \frac{\ln(2)}{t_{1/2}}\), where \(t_{1/2}\) is the half-life of the isotope.
5. Determine the activity (A) of the sample in becquerels (Bq) using the formula A = \(\lambda \times \) number of atoms. To convert the activity to curies (Ci), use the conversion factor 1 Ci = 3.7 x 10^10 Bq.

Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This can occur in various forms, including alpha particles, beta particles, and gamma rays. Understanding this concept is crucial for calculating the activity of a radioactive substance, as it directly relates to the rate at which the substance decays over time.

Activity of a Radioactive Sample

The activity of a radioactive sample is defined as the number of decays per unit time, typically measured in becquerels (Bq) or curies (Ci). One Bq corresponds to one decay per second, while one Ci is equivalent to 3.7 x 10^10 decays per second. This concept is essential for quantifying the radioactivity of a sample, such as the nitrogen-16 in the question.

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², indicates that mass can be converted into energy and vice versa. In nuclear reactions, such as the formation of nitrogen-16 from oxygen capturing a neutron, a small amount of mass is converted into energy, which can affect the stability and decay of the resulting isotope. This principle underlies the processes occurring in nuclear reactors.