Question

How many half-lives does it take a radioactive substance to decay until only one-eighth of the original substance remains?

a
eight
b
two
c
six
d
three
Question 27
The half-life for a 100-gram sample of radioactive element X is 5 days. How much of element X remains after 10 days have passed?

a
75 g
b
100 g
c
50 g
d
25 g

Answer 1

1. To determine how many half-lives it takes for a radioactive substance to decay to one-eighth of its original amount, we can express the remaining quantity after \( n \) half-lives as:

\[
\frac{1}{2^n}
\]

We want to find \( n \) such that:

\[
\frac{1}{2^n} = \frac{1}{8}
\]

Since \( \frac{1}{8} = \frac{1}{2^3} \), we can set:

\[
2^n = 2^3
\]

This implies that:

\[
n = 3
\]

So the answer is **d) three**.

2. For the 100-gram sample of radioactive element X, with a half-life of 5 days, we need to determine how much remains after 10 days. Since 10 days corresponds to 2 half-lives (because \( 10 \div 5 = 2 \)), we can calculate the remaining quantity after each half-life:

- After the first half-life (5 days), the amount remaining is:

\[
\frac{100 \text{ g}}{2} = 50 \text{ g}
\]

- After the second half-life (another 5 days), the amount remaining is:

\[
\frac{50 \text{ g}}{2} = 25 \text{ g}
\]

So after 10 days, \( 25 \) grams of element X remain. Thus, the answer is **d) 25 g**.