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Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately 12 years. That is, every 12 years, the amount of tritium decreases by
50%. If a new tritium EXIT sign contains 25 curies of tritium, approximately how many curies of tritium will remain after 24 years?
Choose 1 answer:
(A) 6.25 curies
(B) 12.5 curies
(c)
25 curies
(D) 30 curies

Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately $12$ years. That is, every $12$ years, the amount of tritium decreases by $50 \%$ . If a new tritium EXIT sign contains $25$ curies of tritium, approximately how many curies of tritium will remain after $24$ years? $\newline$ Choose $1$ answer: $\newline$ (A) $6$ . $25$ curies $\newline$ (B) $\mathbf{1 2 . 5}$ curies $\newline$ (C) $25$ curies $\newline$ (D) $30$ curies

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Find probabilities using combinations and permutations

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Q. Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately

12

years. That is, every

12

years, the amount of tritium decreases by

50 \%

. If a new tritium EXIT sign contains

25

curies of tritium, approximately how many curies of tritium will remain after

24

years?

\newline

Choose

1

answer:

\newline

(A)

6

.

25

curies

\newline

(B)

\mathbf{1 2 . 5}

curies

\newline

(C)

25

curies

\newline

(D)

30

curies

Identify Data: Identify the initial amount of tritium, the total time that has passed, and the half-life of tritium. $\newline$ Initial amount $a$ = $25$ curies $\newline$ Total time $t$ = $24$ years $\newline$ Half-life $h$ = $12$ years
Calculate Half-Lives: Determine the number of half-lives that have passed in the given time period. $\newline$ Number of half-lives = Total time / Half-life $\newline$ Number of half-lives = $\frac{24 \, \text{years}}{12 \, \text{years}}$ $\newline$ Number of half-lives = $2$
Use Half-Life Formula: Use the half-life formula to calculate the remaining amount of tritium. $\newline$ The formula is $y = a \times (\frac{1}{2})^{\frac{t}{h}}$ , where $y$ is the remaining amount, $a$ is the initial amount, $t$ is the total time, and $h$ is the half-life period. $\newline$ Substitute the values into the formula: $y = 25 \times (\frac{1}{2})^2$
Calculate Remaining Quantity: Calculate the remaining quantity of tritium. $\newline$ $y = 25 \times (\frac{1}{2})^2$ $\newline$ $y = 25 \times \frac{1}{4}$ $\newline$ $y = 6.25$

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