Question

Which expression represents the mass of sodium remaining after h half-lives?

S = 0.5(800)h

S = 800(0.5)h

S = 8000.5h
S = 800h + 0.5

Answer 1

To determine the expression that represents the mass of sodium remaining after \( h \) half-lives, we can use the concept of half-life.

The mass remaining after \( h \) half-lives can be calculated using the formula:

\[
S = S_0 \left(0.5\right)^h
\]

where:
- \( S_0 \) is the initial mass,
- \( h \) is the number of half-lives,
- \( S \) is the remaining mass after \( h \) half-lives.

If we assume the initial mass \( S_0 \) is 800 (which seems to be suggested by the options provided), the formula becomes:

\[
S = 800 \left(0.5\right)^h
\]

Now let's check the options:

1. **\( S = 0.5(800)h \)** - This is not correct as it does not represent the exponential decay.
2. **\( S = 800(0.5)^h \)** - This matches our derived formula. This is the correct expression.
3. **\( S = 8000.5h \)** - This is not correct as it also does not represent the exponential decay.
4. **\( S = 800h + 0.5 \)** - This is not correct as it is a linear equation, not an exponential decay.

Thus, the correct expression that represents the mass of sodium remaining after \( h \) half-lives is:

**\( S = 800(0.5)^h \)**.