the mass of cobalt-60 in a sample is found to have decreased from 0.800g to 0.200g in a period of 10.5 years. from this info calculate the half-life of cobalt-60
See your post above.
To calculate the half-life of cobalt-60, we need to use the formula for exponential decay:
Nt = N0 * (1/2)^(t / T)
Where:
- Nt is the amount of remaining substance at time t
- N0 is the initial amount of substance
- t is the time that has passed
- T is the half-life of the substance
We know that the initial mass of cobalt-60 (N0) is 0.800g, and the remaining mass after 10.5 years (Nt) is 0.200g. We can substitute these values into the formula as follows:
0.200g = 0.800g * (1/2)^(10.5 / T)
To solve for T (the half-life), we need to isolate it. Let's start by dividing both sides of the equation by 0.800g:
0.200g / 0.800g = (1/2)^(10.5 / T)
Simplifying, we get:
0.25 = (1/2)^(10.5 / T)
To get rid of the exponent, we can take the logarithm (base 2) of both sides:
log2(0.25) = log2((1/2)^(10.5 / T))
Using the property of logarithms that states logb(a^c) = c * logb(a), we can rewrite the equation as:
-2 = (10.5 / T) * log2(1/2)
Since log2(1/2) is equal to -1, the equation becomes:
-2 = (10.5 / T) * (-1)
Now we can solve for T. Multiply both sides of the equation by -1 and divide by -2:
2 = 10.5 / T
Cross-multiply:
2T = 10.5
Finally, divide both sides of the equation by 2 to isolate T:
T = 10.5 / 2
T = 5.25 years
Therefore, the half-life of cobalt-60 is approximately 5.25 years.