If there are 80 milligrams of a radioactive element decays to 10 milligrams in 30 minutes then what is the elements half life in minutes?
Ok i narrowed it down to either 10 or 30...but im rly confused so if u could help it wuld be grea
80
40 1 min
20 2 min
10 3min
looks like three half lives are in 30 min.
Did you try either of the equations we gave you for the last problem you work. Those equations work perfectly well. What to GUESS at 10 or 30?
It says what is the elements half life in minutes i know that it has 3 half lives and each half life is 10 minutes...but idk what its meanning by the elements half life...like is it all 3 its talking about or whats 1 of the half lives..?
jon,,i really think its option 3, 30!!
The half-life is defined as the time it takes for 1/2 of the material to decay. So they want you to determine the half-life; i.e., how long does it take the element to decay to 1/2 its original mass?
ln(No/N) = kt
ln(80/10) = k(30)
ln 8 = 30k
2.079 = 30k
k=2.079/30 = 0.0693
Then k=0.693/t1/2
solve for t1/2
t1/2= 0.693/0.0693
t1/2 = 10 minutes.
The units for t1/2 will be the same as you used for t in the first equation.
To continue, it takes 10 minutes (1 half-life) to decay from 80 mg to 40 mg; it takes another half-life to decay to 20 mg (another 10 minutes) and it takes a third half-life (another 10 minutes) to decay to 10 mg. The next half life would leave 5 mg, the next half life would leave 2.5 mg, etc. The half-life doesn't change. It's 10 minutes. But the amount changes after each half life. Be sure and post with specific questions if this isn't clear. I hope this helps
it is 10 minutes
To find the half-life of the radioactive element in minutes, you can use the formula:
N = No * (1/2)^(t / t1/2)
Where:
- N is the final amount of the element (10 milligrams)
- No is the initial amount of the element (80 milligrams)
- t is the elapsed time (30 minutes)
- t1/2 is the half-life of the element (unknown)
Plugging in the known values:
10 = 80 * (1/2)^(30 / t1/2)
Simplifying the equation:
1/8 = (1/2)^(30 / t1/2)
To solve for t1/2, take the logarithm of both sides:
log(1/8) = log((1/2)^(30 / t1/2))
Using the logarithmic property, we can bring the exponent down:
log(1/8) = (30 / t1/2) * log(1/2)
Evaluate the logarithms:
-3 = (30 / t1/2) * (-0.301)
Simplify:
3 = (30 / t1/2) * 0.301
Divide both sides by 0.301:
3 / 0.301 = 30 / t1/2
9.96678 = 30 / t1/2
Rearrange the equation to solve for t1/2:
t1/2 = 30 / 9.96678
t1/2 ≈ 3.01 minutes
Therefore, the half-life of the radioactive element is approximately 3.01 minutes.