How much of a 6gram sample of silver-105m would remain after 4 minutes?
Half life=7.2 minutes
k = 0.693/t1/2
Substitute k into the equation below.
ln(No/N) = kt.
No = 6
N = unknown
k = from above
t = 7.2 min
I get approximately 4 g remaining.
Great! But, so that I can understand it in the future, can you tell me what the value of k is a little more clearly? how do you do a subscript of 1/2?
The half life is given in the problem (last line you typed) of 7.2 minutes.
I write a t1/2
To turn on subscript type < followed by sub followed by >. Then type the 1/2. To turn subscript off type < followed by /sub followed by >
To determine the amount of silver-105m that would remain after 4 minutes, we can use the concept of half-life.
The half-life of silver-105m is given as 7.2 minutes. This means that, after every 7.2-minute interval, the amount of the sample will be reduced by half.
Let's calculate the number of half-lives that occur within 4 minutes:
Number of half-lives = 4 minutes / 7.2 minutes per half-life
Number of half-lives ≈ 0.5556 (rounded to 4 decimal places)
Since we can't have a fraction of a half-life, we'll use the concept of fractional decay:
Fractional decay = 0.5^(number of half-lives)
Plugging in the value we calculated above:
Fractional decay = 0.5^(0.5556)
Fractional decay ≈ 0.8829 (rounded to 4 decimal places)
Now, to find the amount remaining after 4 minutes, we need to multiply the initial sample size by the fractional decay:
Remaining amount = Initial sample size × Fractional decay
Remaining amount = 6 grams × 0.8829
Remaining amount ≈ 5.2974 grams (rounded to 4 decimal places)
Therefore, approximately 5.2974 grams of the 6-gram sample of silver-105m would remain after 4 minutes.