the concentration of tritium in the wine is 0.34 times that found in the freshly bottled wines. if the half life of the tritium is 12.3 years, estimate the time elapsed since the wine was bottled. help please. thank you :)
time
= -(half life)*ln(fraction remaining)/ln(2)
= -(12.3)*(0.34)/ln(2)
= 19.1 years.
thanks a lot :)
Cesium-137 has a half life of 30.0 years. If initially there are 8.0 kg of cesium-137 present in a sample, how many kg will remain after 60.0 years?
To estimate the time elapsed since the wine was bottled, we can use the concept of radioactive decay and the formula for calculating the amount of a substance remaining after a certain time.
First, let's define a few variables:
C0 = Initial concentration of tritium in freshly bottled wine
C = Current concentration of tritium in the wine
λ = Decay constant (ln(2)/half-life)
From the given information, we know that the concentration of tritium in the wine is 0.34 times that found in freshly bottled wine. Therefore, we can write the following equation:
C = 0.34 * C0
Now, let's use the formula for radioactive decay:
C = C0 * e^(-λ * t)
where t is the time elapsed since the wine was bottled.
Substituting the value of C from the previous equation, we get:
C0 * 0.34 = C0 * e^(-λ * t)
Divide both sides of the equation by C0:
0.34 = e^(-λ * t)
To solve for t, we need to take the natural logarithm (ln) of both sides of the equation:
ln(0.34) = -λ * t
Rearranging the equation to solve for t:
t = -ln(0.34) / λ
Since we know the half-life of tritium is 12.3 years, we can calculate the decay constant (λ):
λ = ln(2) / half-life = ln(2) / 12.3
Plug in the values:
t = -ln(0.34) / (ln(2) / 12.3)
Using a calculator, you can evaluate this expression to estimate the time elapsed since the wine was bottled.