A radium-226 sample initially contains 0.112mol. How much radium-226 is left in the sample after 6400 years. The half-life of radium-226 is 1600 years.
long way.
k = 0.693/t1/2
ln(No/N) = kt
No = 0.112 mol
N = unknown
k from above.
t = 6400 years.
shorter way.
0.112*(1/2^n)
0.112*(1/2^6400/1600)
0.112*(1/2^4) = N
0.04 is the answer
The half-life of Radium -226 is 1600 years. How much Ra 226 remains in a 30.0 g sample after 6400 years?
To calculate the amount of radium-226 left in the sample after 6400 years, we need to determine the number of half-lives that have passed during this time.
The half-life of radium-226 is 1600 years, meaning every 1600 years, the amount of radium-226 in the sample will be halved. Thus, we can calculate the number of half-lives that have occurred by dividing the total time (6400 years) by the half-life (1600 years):
Number of half-lives = Total time / Half-life
= 6400 years / 1600 years
= 4 half-lives
Now, since each half-life reduces the amount of radium-226 by half, after 4 half-lives, the amount remaining will be 1/2^4 = 1/16 of the original amount.
Therefore, the amount of radium-226 left in the sample after 6400 years is:
0.112 mol * (1/16)
= 0.112 mol * 0.0625
= 0.007 mol
So, there would be approximately 0.007 moles of radium-226 left in the sample after 6400 years.