a) 45.02% of the sample remains after 85 days. Consider how you can use the percent of Ir-192 remaining and the number of days to calculate the mass remaining after 85 days.
k = .693/t1/2
t1/2 should be in days.
Solve for k and substitute in the equation below.
ln(No/N) = kt
No = solve for this
N = 45.02
k from above
t = 85 days
Solve for No which will be 100%.
I should have mentioned that the initial mass is 1.75g
I must be missing something. If you had 1.75g initially and 45.02% remains, then you have 1.75 x 0.4502 = ? g remaining after 85 days. Isn't that right?
To calculate the mass remaining after 85 days using the given percent of Ir-192 remaining, you also need the initial mass of the sample and the decay constant. The decay constant for Ir-192 can be found in its half-life, which is the time it takes for half of the substance to decay.
1. Determine the half-life of Ir-192: Find the half-life of Ir-192, which is the time it takes for half of the substance to decay. Let's assume the half-life of Ir-192 is 74 days. This means that after 74 days, half of the initial sample will have decayed.
2. Calculate the decay constant: The decay constant (λ) can be calculated using the equation: λ = -ln(0.5) / half-life. In this case, λ = -ln(0.5) / 74.
3. Calculate the percent remaining after 85 days: Since 85 days have passed, we know that there is 45.02% of the sample remaining. This implies that the decayed portion is 100% - 45.02% = 54.98%.
4. Calculate the mass remaining: To find the mass remaining after 85 days, you need to know the initial mass of the sample. Let's assume the sample's initial mass is M0.
The general equation for radioactive decay is: M(t) = M0 * exp(-λ * t), where M(t) is the mass remaining after time t. In this case, t is 85 days.
Substitute the given percent remaining (54.98%) into the equation: M(85) = M0 * exp(-λ * 85) = 54.98% * M0.
Rearrange the equation to find M0: M0 = M(85) / (54.98%).
Now, you can calculate the mass remaining after 85 days using the initial mass and the given percent remaining.
Please note that this explanation assumes a constant decay rate and is done for illustrative purposes. In practice, the decay rate might vary slightly due to various factors.