How many grams of a 250- g sample of thorium - 234 would remain after 40 days had passed?
How many days would pass while 44 g of thorium -234 decayed to 4.4 g of thorium - 234?
To calculate the remaining grams of thorium-234 after 40 days, we need to determine the half-life of thorium-234 and use the radioactive decay formula.
The half-life of thorium-234 is approximately 24.1 days. This means that after 24.1 days, half of the thorium-234 will have decayed.
Now, we need to calculate the number of half-lives that have occurred in 40 days. We can do this by dividing the number of days by the half-life:
Number of half-lives = 40 days / 24.1 days
Next, we calculate the remaining fraction of thorium-234:
Remaining fraction = (1/2)^(Number of half-lives)
Finally, we multiply the remaining fraction by the initial sample mass of 250 grams to find the remaining grams:
Remaining grams = Remaining fraction * Initial sample mass
Let's calculate the remaining grams step by step:
Number of half-lives = 40 days / 24.1 days = 1.66
Remaining fraction = (1/2)^(1.66) ≈ 0.467
Remaining grams = 0.467 * 250 grams
Therefore, after 40 days had passed, approximately 116.75 grams of the 250-gram sample of thorium-234 would remain.
To determine how many grams of thorium-234 would remain after 40 days, you need to understand the concept of radioactive decay and use the decay equation. The decay of thorium-234 follows an exponential decay equation.
The decay equation is given by:
N(t) = N₀ * e^(-λt)
Where:
N(t) is the amount of the radioactive substance remaining after time t,
N₀ is the initial amount of the radioactive substance,
e is the base of the natural logarithm (approximately 2.71828), and
λ is the decay constant.
For thorium-234, the decay constant (λ) is approximately 4.908 × 10^(-6) per day.
Initially, you have a 250-gram sample of thorium-234 (N₀ = 250 g), and you want to find N(40), the amount remaining after 40 days.
Plug in the values into the decay equation:
N(40) = 250 * e^(-4.908 × 10^(-6) * 40)
Calculating this equation will give you the amount of thorium-234 left after 40 days.
k = 0.693/t1/2
ln(No/N) = kt
No = 44g
N = 4.4 g
k from above
solve for t.