Please assist me in answer this question
please show me all the formulas used and the units and how to convert them if needed. Thank You.
If the half-life of Ba (140, 56) is 12.75 dyas, how many atoms of (140, 56) Ba will be left after 9 weeks if there were initially 2.4 mol of atoms?
How do I do this???
unless chemistry has its own method here, this looks like an exponential decay problem
the half-life formula is
Amount = a(1/2)^(t/k), where a is the initial amount, and k is the half-life time
in this case
a = 2.4
k = 12.75
and t = 9 weeks = 63 days.
amount = 2.4(1/2)^(63/12.75)
= .07812
Avocadro's constant is the number of molecules per mole:
NA= 6.022*1023 mol-1
Multiplying 0.07812 by NA gives the number of molecules remaining, which equals the number of atoms in this case.
By the way, I do not find the isotope 140.56Ba, nor one that has a half life of 12.75 days.
Yes, Ba140 exists.
http://en.wikipedia.org/wiki/Isotopes_of_barium
Thank you Bob!
To solve this question, you need to use the concept of radioactive decay and the formula for calculating the amount of remaining atoms using the half-life.
Here's the step-by-step solution:
1. Convert the initial amount of atoms in moles to the number of atoms:
To do this, you'll use Avogadro's number, which states that 1 mole of any substance contains 6.022 × 10^23 entities.
So, multiply the initial amount of atoms (2.4 mol) by Avogadro's number to get the number of atoms.
2. Calculate the number of half-lives during the given time period (9 weeks):
Since the half-life of Ba-140 is given as 12.75 days, you need to convert the given time period (9 weeks) to days.
There are 7 days in a week, so multiply 9 weeks by 7 days to get the total number of days.
Number of half-lives = (Total number of days) / (Half-life in days)
3. Calculate the remaining amount of atoms using the formula:
N = N₀ * (1/2)^(Number of half-lives)
where N is the remaining amount of atoms, N₀ is the initial amount of atoms, and ^(Number of half-lives) indicates raising to the power of the number of half-lives.
Plug in the values from the previous steps to calculate the remaining amount of atoms.
4. If needed, convert the remaining amount of atoms back to moles:
Divide the remaining amount of atoms by Avogadro's number to obtain the quantity in moles.
Remember to keep track of the units throughout the calculations.