Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
Question
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Chapter 29, Problem 84P

(a)

To determine

The mass of 40K found in a broccoli stalk containing 300 mg of potassium.

(a)

Expert Solution
Check Mark

Answer to Problem 84P

The mass of 40K found in a broccoli stalk containing 300 mg of potassium is 3.6×108 kg.

Explanation of Solution

In natural occurring of potassium, 0.0117% are radioactive 40K. The atomic mass of potassium is 39.0983 u and 40K is 39.9639985 u. The broccoli stalk contains a mass of m=300 mg, what will be the mass of radioactive 40K.

Write the formula for the number of nuclei

    N=mNAM                                                                                           (I)

Here, N is the number of nuclei, m is the mass, NA is the Avogadro’s number and M is the molar mass.

Conclusion:

Divide the mass of potassium and 40K, and substitute in equation (I) to find the value of m40

m40m=N40M40NANMNA=N40N×M40Mm40=N40N×M40M×m

Substitute 0.0117% for N40N, 300 mg for m  39.0983 u for M  and 39.9639985 u for M40 in above equation to find the value of m40

m40=(0.0117)×39.9639985 u39.0983 u×300×103 kgm40=3.6×108 kg

Thus, the mass of 40K found in a broccoli stalk containing 300 mg of potassium is 3.6×108 kg.

(b)

To determine

The activity of broccoli stalk due to 40K.

(b)

Expert Solution
Check Mark

Answer to Problem 84P

The activity of broccoli stalk due to 40K is 9.5 Bq.

Explanation of Solution

The mass of 40K found in a broccoli stalk containing 300 mg of potassium is m=3.6×108 kg,  and its molar mass of is M=39.9639985 g/mol and its half-life is T1/2=1.248×109 yr . The Avogadro’s number is NA=6.022×1023 nuclei/mol.

Write the formula for half-life

    T1/2=τln2                                                                                           (I)

Here, T1/2 is the half-life and τ is the time constant.

Write the formula for the activity

    R=Nτ                                                                                                (III)

Here, R is the activity.

Conclusion:

Substitute equation (I) and (II) in (III) to solve for R0

R=NτR=mNAln2T1/2M

Substitute 3.6×108 kg for m, 6.022×1023 nuclei/mol for NA, 1.248×109 yr for T1/2 and 39.9639985 g/mol for M in the above equation to find the value of R . [Note: 1 yr=3.156×107 s]

R=3.6×108 kg×6.022×1023 nuclei/mol×ln239.9639985 g/mol×1.248×109 yr×3.156×107 s/yrR=9.5 Bq

Thus, the activity of broccoli stalk due to 40K is 9.5 Bq.

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Chapter 29 Solutions

Physics

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