Palladium-107 undergoes â decay (t1/2 = 6.5 x 105 yr) to form silver-107. How long will it take for 0.150 mol of silver-107 to form from 1.25 mol of palladium-107?
help please...thank you :)
i got 1988280, is it right?
Right, but 1988281 if you take care to round the last digit.
To find out how long it will take for 0.150 mol of silver-107 to form from 1.25 mol of palladium-107, we need to use the concept of half-life.
Given:
Half-life of Palladium-107 (Pd-107) = 6.5 x 10^5 years
Step 1: Determine the number of half-lives that have occurred.
Since each half-life reduces the amount of Pd-107 by half, we can calculate the number of half-lives using the equation:
Number of half-lives (n) = (log base 2) (initial amount of Pd-107 / final amount of Pd-107)
n = log2 (1.25 mol / 0.150 mol)
n ≈ 2.91
Step 2: Calculate the time it takes for 1 half-life.
We know that 1 half-life of Pd-107 is equal to 6.5 x 10^5 years.
So, the time for 1 half-life (t1/2) ≈ 6.5 x 10^5 years
Step 3: Calculate the total time required.
To find the total time required (t) for the given reaction, we multiply the time for 1 half-life by the number of half-lives:
t = n x t1/2
t ≈ 2.91 * 6.5 x 10^5 years
t ≈ 1.89 x 10^6 years
Therefore, it will take approximately 1.89 x 10^6 years for 0.150 mol of Ag-107 to form from 1.25 mol of Pd-107.
To find out how long it will take for 0.150 mol of silver-107 to form from 1.25 mol of palladium-107, we need to use the concept of radioactive decay and the given half-life.
First, let's find the number of moles of silver-107 that is formed from 1.25 mol of palladium-107. Since palladium-107 undergoes β decay, one mole of palladium-107 converts into one mole of silver-107. Therefore, if we have 1.25 mol of palladium-107, we will also have 1.25 mol of silver-107 initially.
Next, we need to determine the fraction of silver-107 that remains after a certain time. This can be calculated using the radioactive decay equation:
N(t) = N₀ * (1/2)^(t/T)
where N(t) is the remaining quantity of a radioactive material at time t, N₀ is the initial quantity, t is the time elapsed, and T is the half-life.
We can rearrange the equation to solve for time (t):
t = T * log₂(N(t) / N₀)
Now, let's plug in the values into the equation:
N(t) = 0.150 mol (the remaining quantity we want)
N₀ = 1.25 mol (initial quantity)
T = 6.5 x 10^5 years (half-life)
t = (6.5 x 10^5 years) * log₂(0.150 mol / 1.25 mol)
Calculating this expression will give us the time required for 0.150 mol of silver-107 to form from 1.25 mol of palladium-107.