The half-life of Radium-223 is 11.43 days. If a sample has a mass of 400 mg, find the mass (in mg) that remains after 6 days
amount = 400(1/2)^(t/11.43), where t is number of days.
so if t = 6
amount = 400(1/2)^(6/11.43)
= 277.996
or appr 278 mg
To find the mass of Radium-223 that remains after 6 days, we need to use the concept of radioactive decay and the half-life of the material.
The half-life of Radium-223 is 11.43 days, which means that after every 11.43 days, the amount of Radium-223 will be reduced by half.
To determine how much Radium-223 remains after 6 days, we can use the formula:
Remaining mass = Initial mass × (0.5)^(time elapsed / half-life)
Let's substitute the given values into the formula:
Remaining mass = 400 mg × (0.5)^(6 days / 11.43 days)
Now, let's calculate:
Remaining mass = 400 mg × (0.5)^(0.525)
To calculate the exponent (0.525), we divide 6 days by the half-life of 11.43 days.
Next, let's compute the expression inside the parentheses:
(0.5)^(0.525) ≈ 0.774
Now, we can find the remaining mass:
Remaining mass ≈ 400 mg × 0.774
Remaining mass ≈ 309.6 mg
Therefore, after 6 days, approximately 309.6 mg of Radium-223 will remain in the sample.