Question

If an 900.0 g sample of radium-226 decays to 225.0 g of radium-226 remaining in 3,200 years, what is the half-life of radium-226? (3 points)

Answer 1

1600 yr

Step-by-step explanation:

The half-life of radium-226 is the time it takes for half of it to decay.

After one half-life, half of the original amount will remain.

After a second half-life, half of that amount will remain, and so on.

We can construct a table as follows:

`\begin{array}{cccc}\textbf{No. of} &\textbf{Fraction} &\textbf{Mass}\\ \textbf{Half-lives} & \textbf{Remaining}&\textbf{Remaining/g}\\0 & 1 &900.0\\\\1 & (1)/(2) &450.0\\\\2 & (1)/(4) & 225.0\\\\3 & (1)/(8) & 112.5\\\\\end{array}`

We see that the mass will drop to 225.0 g after two half-lives.

The mass dropped to 225.0 g in 3200 yr.

If 3200 yr = 2 half lives,

1 half-life = 1600 yr

The decay curve for your sample is shown below. The mass has dropped to half its original value (450 g) after 1600 yr and to one -fourth (225.0 g) after 3200 yr.