Answer:
Half life is the time taken by a radio active isotope to reduce by half of its original amount. Radium-226 has a half life of 1602 years meaning that it would take 1602 years for a mass of radium to reduce by half.
Number of half lives in 9612 years = 9612/1602 = 6 half lives
New mass = Original mass x (1/2)n where n is the number of half lives.
Therefore, New mass= 500 x (1/2)∧6
= 500 x 0.015625
= 7.8125 g
Hence the mass of radium after 9612 years will be 7.8125 grams.
Explanation:
Answer:
[tex]\boxed {\boxed {\sf 6.25 \ grams}}[/tex]
Explanation:
We are asked to find the mass of a sample of radium-226 after half-life decay. We will use the following formula:
[tex]A= A_o *\frac{1}{2}^{\frac{t}{h}}[/tex]
In this formula, [tex]A_o[/tex] is the initial amount, t is the time, and h is the half-life.
For this problem, the initial amount is 200 grams of radium-226, the time is 8,000 years, and the half-life is 1,600 years.
[tex]\bullet \ A_o= 200 \ g \\\\bullet \ t= 8,000 \ \\\bullet \ h= 1,600[/tex]
Substitute the values into the formula.
[tex]A= 200 \ g * \frac{1}{2} ^{\frac{8.000}{1,600}[/tex]
Solve the fraction in the exponent.
[tex]A= 200 \ g * \frac{1}{2}^{5}[/tex]
Solve the exponent.
[tex]A= 200 \ g *0.03125[/tex]
[tex]A= 6.25 \ g[/tex]
In addition, we can solve this another way. First, we find the number of half-lives by dividing the total time by the half-life.
Every half-life, 1/2 of the mass decays. Divide the initial mass in half, then that result in half, and so on 5 times.
After 8,000 years, 6.25 grams of radium-226 remains.
