A sample of a radioactive substance has an initial mass of 320 g. If its half-life is 2 minutes, how much of…

Question

A sample of a radioactive substance has an initial mass of 320 g. If its half-life is 2 minutes, how much of the substance will remain after 10 minutes?

ScanSolve AI Tutor · Accepted Answer

let's solve this radioactive decay problem.

The formula for radioactive decay is:

N = N_0 \left( \frac{1}{2} \right)^n

where:

$N$ is the remaining mass of the radioactive material
$N_0$ is the initial mass of the radioactive material
$n$ is the number of half-lives that have passed

Identify the given values.
Initial mass ( $N_0$ ) = $320 \text{ g}$
Half-life ( $T_{1/2}$ ) = $2 \text{ minutes}$
Total time ( $t$ ) = $10 \text{ minutes}$
Calculate the number of half-lives ( $n$ ).
$n = \frac{\text{Total time}}{\text{Half-life}}$ $n = \frac{10 \text{ minutes}}{2 \text{ minutes}}$ $n = 5$
Substitute the values into the decay formula.
$N = 320 \text{ g} \left( \frac{1}{2} \right)^5$
Calculate the value of $\left( \frac{1}{2} \right)^5$ .
$\left( \frac{1}{2} \right)^5 = \frac{1^5}{2^5} = \frac{1}{32}$
Calculate the remaining mass ( $N$ ).
$N = 320 \text{ g} \times \frac{1}{32}$ $N = \frac{320}{32} \text{ g}$ $N = 10 \text{ g}$
The mass remaining after 10 minutes is $10 \text{ g}$ .

The final answer is $\text{a. 10g}$ .

A sample of a radioactive substance has an initial mass of 320 g. If its half-life is 2 minutes, how much of the substance will remain after 10 minutes?

Answer

Step-by-step solution

Identify the given values.

Calculate the number of half-lives ( $n$ ).

Substitute the values into the decay formula.

Calculate the value of $\left( \frac{1}{2} \right)^5$ .

Calculate the remaining mass ( $N$ ).

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More Physics Questions

A sample of a radioactive substance has an initial mass of 320 g. If its half-life is 2 minutes, how much of the substance will remain after 10 minutes?

Answer

Step-by-step solution

Identify the given values.

Calculate the number of half-lives (nnn).

Substitute the values into the decay formula.

Calculate the value of (12)5\left( \frac{1}{2} \right)^5(21​)5.

Calculate the remaining mass (NNN).

Try one yourself

Still stuck on this one?

More Physics Questions

Calculate the number of half-lives ( $n$ ).

Calculate the value of $\left( \frac{1}{2} \right)^5$ .

Calculate the remaining mass ( $N$ ).