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What is the halflife of sodium 25 if 1.00 gram of a 16.00 gram sample of sodium 25 remains unchanged after 237 seconds?
59.25 seconds
After 1 half-life: 16*(1/2) = 8 g remains
After 2 half-lives: 8*(1/2) = 4g remains
After 3 half-lvies: 4*(1/2) = 2g remains
After 4 half-lives: 2*(1/2) = 1g remains
So after 4 half-lves you have 1 gram of Na25 left. This is also the amount remaining after 237 seconds. Since 4 half-lives have elapsed over 237 seconds, you can divide 237 seconds by 4 to find the half-life of Na25 is 59.25 seconds.
You can also figure it out using the rate of decay formula:
At = Ao*e-kt
where Ao is the initial amount, At is the amount left after some time t. k is the decay constant which is k = ln 2 / t1/2 where t1/2 is the half-life.
In this case Ao = 16g, At = 1g, t=237 sec
Substitute in the formula to solve for k, then take the answer for k and use it in the other formula to solve for the half-life (t1/2):
1 = 16*e-237k
ln (1/16) = ln (e-237k)
-2.7726 = -237k
k = -2.7726/-237 = 0.011699 sec-1
t1/2 = ln 2/k = 0.693147/0.011699 sec-1
t1/2 = 59.25 sec
What else can I help you with?
What percent of a sample of As-81 remains undecayed after 43.2 seconds?
To determine the percentage of As-81 that remains undecayed after 43.2 seconds, you would need to know its half-life. As-81 has a half-life of approximately 46.2 seconds. Using the formula for radioactive decay, after one half-life (46.2 seconds), 50% would remain. Since 43.2 seconds is slightly less than one half-life, a little more than 50% of the sample remains undecayed, but the exact percentage requires calculations based on the exponential decay formula.
What happens to the standard deviation as the sample size increases?
As the sample size increases, the standard deviation of the sample mean, also known as the standard error, tends to decrease. This is because larger samples provide more accurate estimates of the population mean, leading to less variability in sample means. However, the standard deviation of the population itself remains unchanged regardless of sample size. Ultimately, a larger sample size results in more reliable statistical inferences.
What is the half-life of sodium-25 if 1.00 gram of a 16.00-gram sample of sodium-25 remains unchanged?
The half-life of sodium-25 can be determined by the decay of the sample. If 1.00 gram remains from an initial 16.00-gram sample, then 15.00 grams have decayed. This means that 1.00 gram represents ( \frac{1}{16} ) of the original sample, which indicates that the sample has gone through four half-lives (since ( \frac{1}{2^4} = \frac{1}{16} )). Therefore, if the time taken for these four half-lives is known, the half-life can be calculated as one-fourth of that total time.
What percent of a sample of As-81 remains un-decayed after 43.3 seconds?
To determine the percent of As-81 that remains un-decayed after 43.3 seconds, you would need to know its half-life. The half-life of As-81 is approximately 46.2 seconds. Given that 43.3 seconds is slightly less than one half-life, you can use the formula for exponential decay: [ N(t) = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}} ] where ( N_0 ) is the initial quantity, ( t ) is the elapsed time, and ( T_{1/2} ) is the half-life. After 43.3 seconds, about 80% of the original sample of As-81 would remain un-decayed.
A 200 gram sample having a half- life of 12 seconds would have how much remaining after 36 seconds?
To determine the remaining amount of a 200 gram sample after 36 seconds with a half-life of 12 seconds, we first calculate how many half-lives fit into 36 seconds. There are three half-lives in 36 seconds (36 ÷ 12 = 3). Each half-life reduces the sample by half: after the first half-life, 100 grams remain; after the second, 50 grams; and after the third, 25 grams. Therefore, 25 grams of the sample would remain after 36 seconds.
What fraction of an original 20.00gram sample of nitrogen-16 remains unchanged after 36.0 seconds?
2
Which fraction of an original 20.00-gram sample of nitrogen-16 remains unchanged after 36.0 seconds?
Nitrogen-16 has a half-life of about 7.13 seconds. After 36.0 seconds, there would be 3 half-lives. Therefore, 1/2 * 1/2 * 1/2 = 1/8 of the original sample remains unchanged.
What fraction of a sample of N 16 remains undecayed after 43.2 seconds?
1.5% remains after 43.2 seconds.
What part of a radioactive sample remains unchanged after 2 half lives?
After 2 half lives, 25% of the original radioactive sample remains unchanged. This is because half of the sample decays in each half life, so after 1 half life, 50% has decayed, and after 2 half lives, another 50% has decayed, leaving 25% unchanged.
If Astatine-218 has a half-life of 1.6 s Suppose you have a 1.2-g sample of astatine-218 How much of the sample remains unchanged after 6.4 seconds Explain how you solved the problem?
After 1.6 seconds, 0.6 g astatine-218 remains unchanged. This amount is reduced by half to 0.3 g at 3.2 seconds. It is halved again at 4.8 seconds to 0.15 g, and halved once more to 0.075 g unchanged after a total of 6.4 seconds.
Why is the density of a substance independent of sample size?
Density is an intensive quantity which means it is independent of size. This can be seen from the definition of density. Density = mass/volume So if the sample size increases than so does the mass, but the density remains unchanged.
What is the time needed for half of a sample of a radioactive isotope to break down to form daughter isotopes called?
halflife
How much of a 100 gram sample would remain unchanged after two hours?
This would depend on the specific sample and its stability. Without additional information, it is not possible to determine how much of the sample would remain unchanged after two hours.
Thorium-234 has a half-life of 24.1 days. How much of a 100-g sample of thorium-234 will be unchanged after 48.2 days?
Thorium-234 has a half-life of 24.1 days. How much of a 100-g sample of thorium-234 will be unchanged after 48.2 days?
How much of a 100 g sample of thorium 234 will be unchanged after 48.2 days?
After 48,2 days the amount of Th-234 will be 25 g.
How many unchanges atoms would remain after 3 half lives if the initial sample had 600 unchanged atoms?
After 3 half-lives, half of the original sample would remain unchanged. After the 1st half-life: 300 unchanged atoms. After the 2nd half-life: 150 unchanged atoms. After the 3rd half-life: 75 unchanged atoms would remain.
Is a radioactive sample has decayed until only one eighth of the original sample remains unchanged how many half lives have elapsed?
Three half lives have elapsed. This can be determined by calculating how many times the original sample size must be halved to get to one eighth: (1/2) * (1/2) * (1/2) = 1/8.
