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Chapter 21: Q31E (page 1205)

Question: Define the term half-life and illustrate it with an example.

Short Answer

Expert verified

The half-life of a radioactive element is the time it takes for its activity to drop to half of its original activity. A probability is what a half-life is. When half of the atoms have decayed, this is the predicted value.

Step by step solution

01

Introduction

The half-life of a quantity is the time it takes for it to decline to half its original value. In nuclear physics, the word explains how quickly unstable atoms decay radioactively and how long stable atoms survive.

02

Defining half-life

Half-life is the time required for the activity of a radioactive element to fall to half of its initial activity.

Half-life is defined as a probability. It is an expected value when half the number of atoms has decayed.

For example, we can use carbon\({\rm{ - 14}}\)which has a half-life of\({\rm{5730}}\)years. If we take one atom of\({\rm{C - 14}}\), that means either it will decay after\({\rm{5730}}\)years or it will not. But if we conduct this experiment repeatedly, we will see that the atom decays within the half-life\({\rm{50\% }}\)of the time.

If we have\({\rm{50g}}\)of\({\rm{C - 14}}\), after\({\rm{5730}}\)years, we will have\({\rm{25g}}\).

Therefore, the half-life is time for an element to fall to its half weight.

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Most popular questions from this chapter

Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in \({\rm{1941}}\). They proposed that the source of this \({}^{{\rm{239}}}{\rm{Pu}}\) was the capture of neutrons by \({}^{{\rm{238}}}{\rm{U}}\) nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed \({\rm{4}}{\rm{.7 \times 1}}{{\rm{0}}^9}\) years ago?

Question: 13. Complete each of the following equations by adding the missing species:

\(\begin{array}{l}{\bf{(a) }}_{{\bf{13}}}^{{\bf{27}}}{\bf{Al + }}_{\bf{2}}^{\bf{4}}{\bf{Hen }} \to {\bf{? + }}_{\bf{0}}^{\bf{1}}{\bf{n}}\\{\bf{(b) }}_{{\bf{94}}}^{{\bf{239}}}{\bf{Pu + }} \to {\bf{?n}}_{{\bf{96}}}^{{\bf{242}}}{\bf{Cm + }}_{\bf{0}}^{\bf{1}}{\bf{n}}\\{\bf{(c) }}_{{\bf{ 7}}}^{{\bf{14}}}{\bf{\;N + }}_{\bf{2}}^{\bf{4}}{\bf{Hen }} \to {\bf{? + }}_{\bf{1}}^{\bf{1}}{\bf{H}}\\{\bf{(d) }}_{{\bf{92}}}^{{\bf{235}}}{\bf{Un }} \to {\bf{? + }}_{{\bf{55}}}^{{\bf{135}}}{\bf{Cs + 4}}_{\bf{0}}^{\bf{1}}{\bf{n}}\end{array}\)

Question: The following nuclei do not lie in the band of stability. How would they be expected to decay? Explain your answer.

(a) \({}_{{\rm{15}}}^{{\rm{34}}}{\rm{P}}\)

(b) \({}_{{\rm{92}}}^{{\rm{239}}}{\rm{U}}\)

(c) \({}_{20}^{{\rm{38}}}{\rm{Ca}}\)

(d) \({}_{\rm{1}}^{\rm{3}}{\rm{H}}\)

(e) \({}_{94}^{{\rm{245}}}{\rm{Pu}}\)

Calculate the density of the\(_{12}^{24}Mg\)nucleus in\(g/mL\), assuming that it has the typical nuclear diameter of \(1 \times 1{0^{ - 13}}\;cm\)and is spherical in shape.

The isotope \({}_{{\rm{38}}}^{{\rm{90}}}{\rm{Sr}}\) is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a \({\rm{0}}{\rm{.500 - g}}\) sample diminishes to \({\rm{0}}{\rm{.393 g}}\)in \({\rm{10}}{\rm{.0 y}}\). Calculate the half-life.
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