Question

which type of radiation is the most penetrating?
beta particle
alpha particle
x - rays
gamma rays
after 80 days, 7 grams of a radioactive isotope remains from an original 112 - gram sample. what is the half - life of this element?
5 days
10 days
20 days
40 days
80 days

Explanation:

Step1: Recall radiation - penetrating power

Gamma rays have the highest penetrating power among beta particles, alpha particles, and X - rays. Alpha particles can be stopped by a sheet of paper, beta particles can be stopped by a few millimeters of aluminum, while gamma rays require several centimeters of lead or concrete to be significantly attenuated.

Step2: Use radioactive decay formula

The radioactive decay formula is $N = N_0(\frac{1}{2})^{\frac{t}{T_{1/2}}}$, where $N$ is the remaining amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T_{1/2}$ is the half - life. We know that $N = 7$ grams, $N_0=112$ grams, and $t = 80$ days. Substitute these values into the formula: $7 = 112(\frac{1}{2})^{\frac{80}{T_{1/2}}}$. First, simplify the equation: $\frac{7}{112}=(\frac{1}{2})^{\frac{80}{T_{1/2}}}$, so $\frac{1}{16}=(\frac{1}{2})^{\frac{80}{T_{1/2}}}$. Since $\frac{1}{16}=(\frac{1}{2})^4$, then $\frac{80}{T_{1/2}} = 4$.

Step3: Solve for half - life

Cross - multiply the equation $\frac{80}{T_{1/2}} = 4$ to get $4T_{1/2}=80$. Then, divide both sides by 4: $T_{1/2}=\frac{80}{4}=20$ days.

Answer:

1. gamma rays
2. 20 days