Question

The half-life of Rn-222 is 3.823 days. What was the original mass of a sample of this isotope if 0.0500 g remains after 7.646 days?

a) 0.025 g
b) 0.050 g
c) 0.100 g
d) 0.200 g

Answer 1

To find the original mass of a radioactive isotope, we use its half-life. Since 7.646 days is two half-lives of Rn-222, we double the remaining mass twice to find the original mass. The original mass of the Rn-222 sample was 0.200 g.

Step-by-step explanation:

The question pertains to the concept of the half-life of a radioactive isotope, specifically radon-222 (Rn-222). The half-life of an isotope is the time required for half of the radioactive nuclei in a sample to decay. In this case, the half-life of Rn-222 is given as 3.823 days. To find the original mass of the sample when 0.0500 g remains after 7.646 days, one must realize that 7.646 days is exactly two half-lives (since 7.646 is approximately 2 times 3.823).

After one half-life (3.823 days), the mass would have been reduced to half of its original value, and after two half-lives (7.646 days), it would be halved again. We start with the remaining mass:

• After 7.646 days (2 half-lives): 0.0500 g
• After 3.823 days (1 half-life): 0.0500 g × 2 = 0.100 g
• Original mass: 0.100 g × 2 = 0.200 g

Therefore, the original mass of the sample was 0.200 g before any decay occurred, which corresponds to answer choice (d).