Question

Radium–226 has a half-life of 1,600 years. If we start with 8,000 atoms of radium, how much would remain after 3,200 years?

A. 0 atoms
B. 1,000 atoms
C. 2,000 atoms
D. 4,000 atoms
E. 8,000 atoms

Answer 1

After 3,200 years, 2,000 atoms of radium will remain.

Step-by-step explanation:

The half-life of radium-226 is 1,600 years. This means that after every 1,600 years, half of the radium atoms will decay. Starting with 8,000 atoms of radium, we can determine how many atoms will remain after 3,200 years.

Since 3,200 years is equal to 2 half-lives (1,600 × 2 = 3,200), we can calculate the remaining atoms as follows:

1. After the first half-life: 8,000 / 2 = 4,000 atoms remain
2. After the second half-life: 4,000 / 2 = 2,000 atoms remain

Therefore, after 3,200 years, 2,000 atoms of radium will remain.