A radioactive element sodium-24 has a half-life of 17 hours and is used to help locate obstructions in blood flow. A procedure requires 1.2 grams and is scheduled to take place in 24 hours.
At what rate is the sodium-24 decaying?
What is the minimum amount of sodium-24 that must be on hand now?
2007-11-14 17:34:50 · 2 answers · asked by Mixed Asian 5 in Science & Mathematics ➔ Mathematics
b is before, a is after,
a = b(0.5)^(t/17) with t measured in hours
a = b[(0.5)^(1/17)]^t
and [...] is the rate of decay per hour,
0.5^(1/17) = 0.96005, which is a loss of 4% per hour.
if we need a to be 1.2 g, with t = 24, b must be....
1.2 = b(0.96)^24
b = 1.2 / (0.96)^24 = 3.1927 g
2007-11-14 17:44:45 · answer #1 · answered by Philo 7 · 1⤊ 0⤋
half-life= ln2/decay constant
decay constant= ln2/17
Let initial amt of sodium-24 be x
Amt of sodium-24 24hours later
= x*(1/2)^(24/17) >or= 1.2
x>or=3.1927g
min amt =3.1927g
2007-11-14 17:49:06 · answer #2 · answered by ghost whisperer 3 · 0⤊ 0⤋