What total mass of a 16 gram sample of 60co will remain unchanged after 15.8 years?
k = 0.693/t1/2
Substitute t1/2 (in years) into the above and calculate k. Then substitute k into the below equation and solve for N.
ln(No/N) = kt
No = 16
N = solve for this.
k = from above.
t = 15.8 years.
The answer is close to 2 grams.
Hmm, let me think about that. Well, based on my calculations, I would say that the total mass of a 16 gram sample of 60Co that remains unchanged after 15.8 years is...wait for it...still 16 grams! It's not called "unchanged" for nothing, you know!
To find the total mass of a 16 gram sample of 60Co that remains unchanged after 15.8 years, you need to calculate the decay of the substance using its half-life.
The half-life of 60Co is 5.27 years, which means that after every 5.27 years, half of the substance will decay.
First, determine how many half-lives have passed in 15.8 years.
Number of half-lives = (15.8 years) / (5.27 years/half-life)
Number of half-lives = 2.997
Since we cannot have a fraction of a half-life, we can round this value to 3 half-lives.
Now, calculate the remaining mass using the half-life information.
Remaining mass = initial mass * (1/2)^(number of half-lives)
Remaining mass = 16 grams * (1/2)^3
Remaining mass = 16 grams * (1/8)
Remaining mass = 2 grams
Therefore, the total mass of a 16 gram sample of 60Co that remains unchanged after 15.8 years is 2 grams.
To determine the total mass of a 16 gram sample of 60Co that remains unchanged after 15.8 years, we need to understand the concept of half-life.
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In the case of 60Co, its half-life is approximately 5.3 years.
Using this information, we can calculate the number of half-lives that occur within 15.8 years. Since each half-life is 5.3 years, we divide 15.8 by 5.3:
15.8 years / 5.3 years = 2.98 half-lives
This means that after 15.8 years, 60Co will have gone through approximately 2.98 half-lives.
Now we can calculate the remaining mass. Since each half-life reduces the mass by half, the remaining mass after 2.98 half-lives can be calculated using the half-life formula:
Remaining Mass = Initial Mass * (1/2)^(number of half-lives)
Given that the initial mass is 16 grams and the number of half-lives is 2.98, we can substitute these values into the formula:
Remaining Mass = 16 grams * (1/2)^(2.98)
Calculating this expression, we find that the remaining mass of the 16 gram sample of 60Co after 15.8 years is approximately 4.37 grams.