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Chapter 42: Q 30 Exercise (page 1236)

What is the total energy (in MeV) released in the beta-minus
decay of ²⁴Na?

Short Answer

Expert verified

Hence, the energy is $5.513489 MeV$

Step by step solution

Given information

$Δ m = 0.005919 u m ({}^{24}N_{a}) = 23.990961 u m ({}^{24}M_{g}) = 23.985042 u$

Explanation

The decay is given as:

${}^{24}N_{a} \to {}^{24}M_{g} + e^{-} + \bar{v}$

Formula for finding energy is:

$E = Δ m c^{2}$

Calculations

Substituting the values:

$E = (0.005919 u) c^{2} \times \frac{931.49 \frac{MeV}{c^{2}}}{1 u} E = 5.513489 MeV$

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Most popular questions from this chapter

The uranium isotope ${}^{238}U$ is naturally present at low levels in many soils. One of the nuclei in the decay series of ${}^{238}U$ is the radon isotope ${}^{222}R n$ , which decays by emitting a localid="1650487447445" $5.50 M e V$ alpha particle with localid="1650487458663" $t_{1 / 2} = 3.82$ days. Radon is a gas, and it tends to seep from soil into basements. The Environmental Protection Agency recommends that homeowners take steps to remove radon, by pumping in fresh air, if the radon activity exceeds $4 p C i p e r l i t e r$ of air.

a. How many ${}^{222}R n$ atoms are there in $1 m^{3}$ of air if the activity is $4 \frac{p C i}{L}$ ?

b. The range of alpha particles in air is $\approx 3 c m$ . Suppose we model a person as a $180 - c m$ -tall, $25 - c m$ -diameter cylinder with a mass of $65 k g$ . Only decays within $3 c m$ of the cylinder can cause exposure, and only $\approx 50 %$ , of the decays direct the alpha particle toward the person. Determine the dose in $m S v p e r y e a r$ for a person who spends the entire year in a room where the activity is $4 p C i / L$ .

c. Does the EPA recommendation seem appropriate? Why?

a. What is the smallest value of $A$ for which there are two stable nuclei? What are they?

b. For which values of $A$ less than this are there no stable nuclei?

Nucleus A decays into nucleus B with a half-life of 10 s. At

t = 0 s, there are 1000 A nuclei and no B nuclei. At what time

will there be 750 B nuclei?

Calculate the chemical atomic mass of silicon.

The half-life of the uranium isotope ${}^{235}U$ is $700$ million years. The earth is approximately localid="1650486537957" $4.5$ billion years old. How much more ${}^{235}U$ was there when the earth formed than there is today? Give your answer as the then-to-now ratio.

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What is the total energy (in MeV) released in the beta-minusdecay of 24Na?

Short Answer

Step by step solution

Given information

Explanation

Calculations

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What is the total energy (in MeV) released in the beta-minus
decay of ²⁴Na?