Questions: A radioactive isotope has a half-life of about 9 years, which means that if it starts with 1 kg of this isotope, 0.5 kg will decay during the first 9 years. Determine how much will decay during the next 9 years.

Solution Steps

The half-life of a radioactive isotope is the time required for half of the isotope to decay. In this problem, the half-life is given as 9 years. This means that every 9 years, half of the remaining isotope will decay.

Initially, we have 1 kg of the isotope. After the first 9 years, half of it will decay, leaving us with:

\[ \text{Remaining isotope after 9 years} = \frac{1}{2} \times 1 \, \text{kg} = 0.5 \, \text{kg} \]

Now, we need to determine how much of the remaining 0.5 kg will decay in the next 9 years. Again, half of the remaining isotope will decay:

\[ \text{Decay during the next 9 years} = \frac{1}{2} \times 0.5 \, \text{kg} = 0.25 \, \text{kg} \]

Final Answer