A sample of sodium-24 with an activity of 12 mCi is used to study the rate of blow flow in the circulatory system. If sodium -24 has a half-life of 15 hours, what is the activity of the sodium after 2.5 d ?
You can do this two ways.
No/N = 2n
12/N = 22.5*24/15
12/N = 16
N = 12/16 = 0.75 mCi after 2.5 days.
Other way.
Calculate k from 0.69315/15 = 0.04621 and substitute into the following:
ln(No/N) = kt
No = 12
N = ??
k = from above.
t = 2.5 days in hours is 2.5 x 24 = 60
ln(12/N) = 0.69315/60
Solve for N = 0.75 mCi.
Well, well, well, we've got some scientific fun going on here! Let's do some math with a sprinkle of humor.
So, we know that sodium-24 has a half-life of 15 hours, right? Now, I'll let you in on a "half-life hack" – after each half-life, the activity is cut in half, just like that time you cut your pizza and suddenly had half the amount!
Alright, let's start crunching some numbers. Since 1 day = 24 hours, 2.5 days will be 60 hours. And if each half-life is 15 hours, we can divide 60 by 15 to find how many half-lives have passed.
*starts calculating with an imaginary abacus*
60 divided by 15 equals...4! We've got ourselves 4 half-lives!
Now, since we're in a "half-life party," we halve the original activity (12 mCi) for each half-life. Let's do this!
First half-life: 12 mCi / 2 = 6 mCi
Second half-life: 6 mCi / 2 = 3 mCi
Third half-life: 3 mCi / 2 = 1.5 mCi
Fourth half-life: 1.5 mCi / 2 = 0.75 mCi
And there it is! After 2.5 days, the activity of the sodium-24 sample is approximately 0.75 mCi. So, if you're studying the rate of blood flow and using this sodium-24, make sure you factor in that decay!
Remember to handle radioactive materials responsibly, folks! Safety first, science second, and humor always.
To calculate the activity of the sodium-24 after 2.5 days, we first need to convert days into hours since the half-life of sodium-24 is given in hours.
Given:
Activity of sodium-24 = 12 mCi
Half-life of sodium-24 = 15 hours
Now, let's convert 2.5 days into hours:
1 day = 24 hours
2.5 days = 2.5 * 24 = 60 hours
Next, we need to determine the number of half-lives that have passed in 60 hours. Since the half-life of sodium-24 is 15 hours, we divide the total time (60 hours) by the half-life:
Number of half-lives = Total time / Half-life = 60 hours / 15 hours = 4 half-lives
Every half-life, the activity of a radioactive substance decreases by half. So, after 4 half-lives, the activity will decrease by a factor of 2 raised to the power of 4 (2^4).
Activity after 2.5 days = Initial activity * (1/2)^(Number of half-lives)
Activity after 2.5 days = 12 mCi * (1/2)^4
Activity after 2.5 days = 12 mCi * (1/16)
Activity after 2.5 days = 0.75 mCi
Therefore, the activity of the sodium-24 after 2.5 days is 0.75 mCi.
Ln(Ao/A)=kt/2.30
ln(12/A)=0.0462*2.5/2.30
A=21.47