If in August 1911 Mme. Curie prepared an international standard containing
20.00 mg of RaCl2, what will the radium content of this standard be in August 2010?
Halflife of radium 222 is 1601 years.
content=20mg*e^(-ln2*t/1601) and t= 99 years
content= 20.00 e^(-4.286E-2)=1.168 check that.
Thanks!
To determine the radium content of the standard in August 2010, we need to consider the radioactive decay of radium over time. Radium-226 has a half-life of approximately 1,600 years.
To calculate the radium content after a certain number of half-lives, we can use the formula:
Final Amount = Initial Amount * (1/2)^(t / half-life)
Where:
- Final Amount is the amount of radium at the end of the given time (August 2010 in this case)
- Initial Amount is the starting amount of radium (20.00 mg in August 1911)
- t is the time that has passed since the starting point in years (99 years in this case)
- Half-life is the half-life of radium-226 (1,600 years)
Using this formula, we can calculate the radium content in August 2010 as follows:
Final Amount = 20.00 mg * (1/2)^(99 / 1,600)
Let's calculate this:
Final Amount = 20.00 mg * (1/2)^(0.0619)
To calculate (1/2)^(0.0619), we raise 0.5 to the power of 0.0619:
(1/2)^(0.0619) ≈ 0.998
Final Amount ≈ 20.00 mg * 0.998
Final Amount ≈ 19.96 mg
Therefore, in August 2010, the radium content of the standard prepared by Mme. Curie would be approximately 19.96 mg.