What is the approximate percentage of a 10C sample left after a 75 year old male walks one lap around the gym, given its half life is 20 seconds?

What is the approximate percentage of a 10C sample left after a 75 year old male walks one lap around the gym, given its half life is 20 seconds?

• A. 5%
• B. 10%
• C. 25%
• D. 75%

Answer: (C)

To calculate the remaining percentage of a 10C sample after a 75-year-old male walks one lap around the gym, given the half-life of the sample is 20 seconds, we first need to determine the number of half-lives that have passed during this period. First, convert 75 years into seconds: - 75 years = 75 x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute - This calculation results in approximately 2,365,200,000 seconds. Next, we calculate the number of half-lives that fit into this time: - Number of half-lives = Total time in seconds / Half-life - Number of half-lives = 2,365,200,000 seconds / 20 seconds = 118,260,000 half-lives. The fraction of the sample remaining after a certain number of half-lives can be calculated using the formula: \[ \text{remaining fraction} = \left( \frac{1}{2} \right)^{n} \] where \( n \) is the number of half-lives. Since \( n \) is extremely large (118,260,000), this means that the

To calculate the remaining percentage of a 10C sample after a 75-year-old male walks one lap around the gym, given the half-life of the sample is 20 seconds, we first need to determine the number of half-lives that have passed during this period.

First, convert 75 years into seconds:

• 75 years = 75 x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute

• This calculation results in approximately 2,365,200,000 seconds.

Next, we calculate the number of half-lives that fit into this time:

• Number of half-lives = Total time in seconds / Half-life

• Number of half-lives = 2,365,200,000 seconds / 20 seconds = 118,260,000 half-lives.

The fraction of the sample remaining after a certain number of half-lives can be calculated using the formula:

[ \text{remaining fraction} = \left( \frac{1}{2} \right)^{n} ]

where ( n ) is the number of half-lives.

Since ( n ) is extremely large (118,260,000), this means that the