Question

"20.0 grams of element C decays until only 5.00 grams is left. If this occurs over a 50.0 year period, what is the half-life of C?

A) 10.0 years
B) 12.5 years
C) 25.0 years
D) 100.0 years"

Answer 1

To find the half-life of element C, we note that the mass goes from 20.0 grams to 5.0 grams in 50 years, indicating two half-life periods have occurred. Thus, each half-life is 25.0 years (50 years / 2).

Step-by-step explanation:

The problem presents a radioactive decay situation and asks us to find the half-life of element C. With an initial amount of 20.0 grams and 5.00 grams remaining after 50.0 years, we can calculate the number of half-lives that have occurred using the following steps:

• Determine the number of times the mass has been halved: 20.0g to 10.0g (1 half), 10.0g to 5.0g (2 halves).
• Since the mass has been halved twice over 50.0 years, each half-life corresponds to 50.0 years / 2 = 25.0 years.

Therefore, the correct answer is (C) 25.0 years. This is the time it takes for half of the radioactive isotopes of element C to decay.