Tritium (half-life= 12.3 y) is used to verify the age of expensive brandies. If an old brandy contains only 1/16 of the tritium present in new brandy, how long ago was it produced?
49 y pr 49.2
in 12.3 years, new brandy contains 1/2 of the original tritium.
in 24.6 years, new brandy contains 1/4 of the original tritium.
in 36.9 years, new brandy contains 1/8 of the tritium.
In how many years will it contain 1/16 of the original tritium?
Well, well, it seems we have a case of brandy and radioactivity! Let's channel our inner chemist and figure this out!
If the old brandy contains only 1/16th of the tritium present in new brandy, we can use the concept of half-lives to determine the age. Since tritium's half-life is 12.3 years, we'll use that information.
If the old brandy has 1/16th of the original tritium, that means it has undergone four half-lives (2^4 = 16). So, if we multiply 12.3 years (the half-life) by 4, we get 49.2 years!
So, drumroll please... it seems the brandy was produced around 49.2 years ago. Cheers to aged brandy and radioactive calculations! Just remember, Clown Bot is great at math, but not so great at drinking brandy.
To determine how long ago the old brandy was produced, we can use the concept of half-life and the given information that the half-life of tritium is 12.3 years.
The half-life of a radioactive substance is the amount of time it takes for half of the substance to decay.
Given that the old brandy contains only 1/16th of the tritium present in new brandy, it means that the amount of tritium in the old brandy has gone through 4 half-lives.
We can set up an equation to solve for the time it takes for 1/16th of the tritium to decay:
(1/2)^n = 1/16
Where n represents the number of half-lives.
To solve for n, we can take the logarithm of both sides of the equation:
log2((1/2)^n) = log2(1/16)
n * log2(1/2) = log2(1/16)
n * (-1) = -4
n = 4
Therefore, the old brandy was produced 4 half-lives ago. To find the time, we multiply the number of half-lives by the half-life duration:
Time = 4 * 12.3 years = 49.2 years
Thus, the old brandy was produced approximately 49.2 years ago.
To determine how long ago the old brandy was produced, we need to use the concept of half-life. The half-life of Tritium is given as 12.3 years, meaning that after 12.3 years, half of the initial amount of Tritium will have decayed.
Let's assume the initial amount of Tritium in the new brandy is X.
According to the given information, the old brandy contains only 1/16 of the Tritium present in the new brandy. So, the amount of Tritium in the old brandy would be 1/16 * X.
We need to find out how many half-lives have passed to reduce the amount of Tritium from X to 1/16 * X.
To calculate the number of half-lives, we can use the following formula:
(Number of half-lives) = (Time elapsed) / (Half-life)
Let's plug in the values:
(Number of half-lives) = (Time elapsed) / 12.3
(Number of half-lives) = log2(Initial amount / Final amount)
(Number of half-lives) = log2(X / (1/16 * X))
Simplifying the equation:
(Number of half-lives) = log2(16)
(Number of half-lives) = 4
Therefore, 4 half-lives have passed to reduce the Tritium amount from X to 1/16 * X.
Since the half-life of Tritium is 12.3 years, the time required for 4 half-lives is:
(4 half-lives) * (12.3 years per half-life) = 49.2 years
Therefore, the old brandy was produced approximately 49.2 years ago.