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Chapter 24: Q24.77P (page 1105)

How many joules are released when $1.5$ mol of $239$ Pu decays, if each nucleus releases $5.243$ MeV?

Short Answer

Expert verified

The joules released are ${7.587×10}^{11} J$ .

Step by step solution

01

To find how many joules are released

- ${1.5 mol of}^{239} Pu$ decays

- each nucleus releases $5.243MeV$

First, we need to calculate the number of nuclei in $1.5 molof {}^{239}{Pu}$

$Numberofnuclei = 1.50 mol \times \frac{{6.022×10}^{23} nuclei}{1 mol} = 9.033× 10^{23} nuclei$

Total energy released in $MeV$ is

$Total energy = {9.033×10}^{23} nuclei×5.243 \frac{MeV}{nuclei} = {4.736×10}^{24} MeV$

- ${1MeV = 1.602×10}^{- 13} J$

Therefore, the number of joules released is

${4.736×10}^{24} MeV = {4.736×10}^{24} MeV× \frac{{1.602×10}^{- 13} J}{1MeV} = {7.587×10}^{11} J$

Hence the joules released are ${7.587×10}^{11} J$

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Most popular questions from this chapter

Question: ${}^{237}N p$ is the parent nuclide of a decay series that starts with $α$ -emission, followed by $β^{-}$ emission, and then two more emissions. Write a balanced nuclear equation for each step?

The ${}^{80}{Br}$ nuclide decays either by decay or by electron capture.

(a) What is the product of each process?

(b) Which process releases more energy? (Masses of atoms: ${}^{80}{Br}$ = $79.918528$ amu; ${}^{80}{Kr}$ = $79.916380$ amu; ${}^{80}{Se} = 79.916520$ amu; neglect the mass of electrons involved because these are atomic, not nuclear, masses.)

If $6 .40 \times 10^{- 9} mol$ of $^{176} W$ emits $1 .07 \times 10^{15} β^{+}$ in $1 .00 h$ , what is the decay constant?

Elements $104,105,and106$ have been named rutherfordium (Rf), dubnium (Db), and seaborgium (Sg), respectively. These elements are synthesized from californium- $249$ by bombarding with carbon- $12$ , nitrogen- , and oxygen- $18$ nuclei, respectively. Four neutrons are formed in each reaction as well.

(a) Write balanced nuclear equations for the formation of these elements.

(b) Write the equations in shorthand notation.

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(a) How many rads did the animal receive?

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