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Chapter 24: Q24.45 P (page 1104)

Due to decay of $^{40} K$ , cow鈥檚 milk has a speci铿乧 activity of about ${6x10}^{-11}$ mCi per milliliter. How many disintegrations of $^{40} K$ nuclei are there per minute in an $8.0$ -oz glass of milk?

Short Answer

Expert verified

The number of disintegrations per minute is_{$31.5 d / min$}

Step by step solution

01

Specific activity

Specific activity of a radionuclide is defined as the activity per its quantity.

02

Calculation

- The specific activity of cow's milk is_{$6 脳 10^{鈭� 11} mCi / mL$ $6 脳 10^{鈭� 11} mCi / mL$}

-_{${1颁颈=3.70脳10}^{10} d/s$} (disintegrations per second)

-_{$1 鈥尘颁颈 = 3.70 脳 10^{7} d / s$}

We have to find the number of disintegrations of $^{40} K$ nuclei per min, in $8.0 鈥夆赌塷锄$ glass of milk.

First, let us convert the volume of the glass of milk, from oz to _{data-custom-editor="chemistry" $mL$}

_{$\begin{matrix} 痴=8.0辞锄脳 \frac{29.5735mL}{1oz} \\ =236.59mL \end{matrix}$}

Calculate the number of disintegrations:

_{$\begin{matrix} 础肠迟颈惫颈迟测=厂辫别肠颈蹿颈肠补肠迟颈惫颈迟测脳痴 \\ {=6脳10}^{-11} mCi 脳 236.59mL \\ {=1.419脳10}^{-8} mCi \\ {=1.419脳10}^{-8} 尘颁颈脳 \frac{{3.70脳10}^{7} d/s}{1mCi} \end{matrix}$}

On further simplification,

_{$\begin{array}{l} Activity=0.525d/s \\ =0.525 \frac{d}{s} 脳 \frac{60s}{1min} \\ =31.5d/min \end{array}$}

Hence, the number of disintegrations per minute is $31.5 d / min$

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