Radioactive Decay: Sodium-22 Half-Life Calculation

What is the remaining mass of 72.5 g of sodium-22 after 15.6 years?

Sodium-22 remain : 1.13 g

Radioactive decay is a natural process in which unstable atomic nuclei lose energy by emitting radiation. One way to measure the rate of radioactive decay is by determining the half-life of a radioactive substance. Half-life is the time it takes for half of the initial amount of a radioactive substance to decay.

When calculating the remaining mass of a radioactive substance after a certain period of time, we can use the formula:

Nt = N₀ (1/2)^(T/t 1/2)

Where:

Nt = the remaining mass of the substance after time T

N₀ = the initial mass of the substance

T = duration of decay

t 1/2 = half-life of the substance

In the case of 72.5 g of sodium-22 after 15.6 years with a half-life of 2.60 years, the calculation is as follows:

Nt = 72.5 * (1/2)^(15.6/2.6)

Nt = 72.5 * (1/2)^6

Nt = 1.13 g

Therefore, after 15.6 years, the remaining mass of 72.5 g of sodium-22 will be 1.13 g.