Answer:
the correct answer is: 1 hour 30 minutes.
Step-by-step explanation:
A radioisotope is a radioactive isotope, which is an unstable form of an element that decays over time by emitting radiation. Radioisotopes are used in various scientific, medical, and industrial applications, including radioactive dating, medical imaging, and cancer treatment.
Now, let's calculate the half-life of the radioisotope based on the given information:
At 1 pm, the activity of the radioisotope is 700 counts per minute.
By 4 pm, the activity has fallen to 175 counts per minute.
The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. In this case, the initial activity was 700 counts per minute, and after 3 hours (from 1 pm to 4 pm), it has decreased to 175 counts per minute.
To calculate the half-life, we need to determine how many times the initial activity (700 counts) is reduced to half (350 counts) over the 3-hour period:
Initial Activity (700 counts) -> Half (350 counts) -> Half (175 counts)
The activity is reduced to half twice during this 3-hour period. Therefore, the half-life of the radioisotope is the time it takes to reduce its activity by half, which is 1.5 hours or 1 hour and 30 minutes.
So, the correct answer is: 1 hour 30 minutes.