Chapter 24: Q24.45 P (page 1104)

Due to decay of $^{40} K$ , cow’s milk has a speciﬁc 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

Specific activity

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

Calculation

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

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

-_{$1 mCi = 3.70 \times 10^{7} d / s$}

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

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

_{$\begin{matrix} V=8.0oz× \frac{29.5735mL}{1oz} \\ =236.59mL \end{matrix}$}

Calculate the number of disintegrations:

_{$\begin{matrix} Activity=Specificactivity×V \\ {=6×10}^{-11} mCi \times 236.59mL \\ {=1.419×10}^{-8} mCi \\ {=1.419×10}^{-8} mCi× \frac{{3.70×10}^{7} d/s}{1mCi} \end{matrix}$}

On further simplification,

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

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

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Due to decay of $^{40} K$ , cow’s milk has a speciﬁc 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

Step by step solution

Specific activity

Calculation

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Due to decay of 40K, cow’s milk has a speciﬁc activity of about6x10-11 mCi per milliliter. How many disintegrations of 40K nuclei are there per minute in an8.0 -oz glass of milk?

Short Answer

Step by step solution

Specific activity

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Chemical Analysis

Organic Chemistry

The Earths Atmosphere

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Ionic and Molecular Compounds

Study anywhere. Anytime. Across all devices.

Due to decay of $^{40} K$ , cow’s milk has a speciﬁc 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?