Question

a radioactive element has a half - life of six days. what is the approximate decay rate of the element after the first day?
0.9%
1.5%
8.3%
10.9%

Explanation:

Step1: Recall the radioactive - decay formula

The formula for radioactive decay is $N = N_0(\frac{1}{2})^{\frac{t}{T_{1/2}}}$, where $N$ is the amount of the substance at time $t$, $N_0$ is the initial amount, and $T_{1/2}$ is the half - life. Let the initial amount $N_0 = 1$. After $t = 1$ day and $T_{1/2}=6$ days, we have $N = (\frac{1}{2})^{\frac{1}{6}}$.

Step2: Calculate the amount remaining

$N = (\frac{1}{2})^{\frac{1}{6}}\approx0.891$.

Step3: Calculate the decay rate

The decay rate $r$ is given by $r=(1 - N)\times100\%$. Substituting $N\approx0.891$ into the formula, we get $r=(1 - 0.891)\times100\% = 10.9\%$.

Answer:

10.9%