Please assist me in answer this question

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???

Answer 1

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

Answer 2

Avocadro's constant is the number of molecules per mole:
N_A= 6.022*10²³ mol^-1
Multiplying 0.07812 by N_A 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.

Answer 3

Yes, Ba140 exists.
http://en.wikipedia.org/wiki/Isotopes_of_barium

Answer 4

Thank you Bob!