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Chapter 21: Problem 20

Each of the following nuclei undergoes either beta decay or positron emission. Predict the type of emission for each: (a) \({ }_{38}^{90} \mathrm{Sr}\) (b) \({ }_{38}^{85} \mathrm{Sr}\) (d) sulfur-30. (c) potassium- 40 ,

Short Answer

Expert verified
(a) Sr-90 will undergo beta decay. (b) Sr-85 will undergo beta decay. (c) Sulfur-30 will undergo positron emission. (d) Potassium-40 can undergo both beta decay and positron emission, but beta decay occurs more frequently (89% of the time).

Step by step solution

01

(a) Sr-90

Strontium-90 has 38 protons and 90-38=52 neutrons. The neutron/proton ratio is 52/38=1.37, which is higher than the stable ratio for lighter elements (around 1), indicating that it has too many neutrons relative to protons. Thus, beta decay is more likely to occur for Sr-90, converting a neutron into a proton and stabilizing the nucleus.
02

(b) Sr-85

Strontium-85 has 38 protons and 85-38=47 neutrons. The neutron/proton ratio is 47/38=1.24, which is closer to the stable ratio for lighter elements. However, it still has slightly more neutrons than stable nuclei with this mass number, so beta decay is more likely to occur for Sr-85, converting a neutron into a proton and stabilizing the nucleus.
03

(c) Sulfur-30

Sulfur-30 has a atomic number of 16 (since sulfur is the 16th element in the periodic table), so it has 16 protons and 30-16=14 neutrons. The neutron/proton ratio is 14/16=0.875, which is lower than the stable ratio for lighter elements, indicating that it has too few neutrons relative to protons. Thus, positron emission is more likely to occur for Sulfur-30, converting a proton into a neutron and stabilizing the nucleus.
04

(d) Potassium-40

Potassium-40 has an atomic number of 19 (since potassium is the 19th element in the periodic table), so it has 19 protons and 40-19=21 neutrons. The neutron/proton ratio is 21/19=1.11, which is slightly higher than the stable ratio for lighter elements, but still close. In this case, both beta decay and positron emission can stabilizing the nucleus, with beta decay leading to the formation of Calcium-40 and positron emission leading to the formation of Argon-40. In reality, both types of decay occur, but positron emission occurs around 11% of the time and beta decay around 89% of the time.

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Most popular questions from this chapter

Methyl acetate \(\left(\mathrm{CH}_{3} \mathrm{COOCH}_{3}\right)\) is formed by the reaction of acetic acid with methyl alcohol. If the methyl alcohol is labeled with oxygen-18, the oxygen-18 ends up in the methyl acetate: (a) Do the \(\mathrm{C}-\mathrm{OH}\) bond of the acid and the \(\mathrm{O}-\mathrm{H}\) bond of the alcohol break in the reaction, or do the \(\mathrm{O}-\mathrm{H}\) bond of the acid and the \(\mathrm{C}-\mathrm{OH}\) bond of the alcohol break? (b) Imagine a similar experiment using the radioisotope \({ }^{3} \mathrm{H}\), which is called tritium and is usually denoted T. Would the reaction between \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(\mathrm{TOCH}_{3}\) provide the same information about which bond is broken as does the above experiment with \(\mathrm{H}^{18} \mathrm{OCH}_{3}\) ?

Which of the following statements about the uranium used in nuclear reactors is or are true? (i) Natural uranium has too little \({ }^{235} \mathrm{U}\) to be used as a fuel. (ii) \({ }^{238} \mathrm{U}\) cannot be used as a fuel because it forms a supercritical mass too easily. (iii) To be used as fuel, uranium must be enriched so that it is more than \(50 \%^{235} \mathrm{U}\) in composition. (iv) The neutron-induced fission of \({ }^{235} \mathrm{U}\) releases more neutrons per nucleus than fission of \({ }^{238} \mathrm{U}\)

Which are not classified as ionizing radiation: gamma rays, beta particles, radio waves used in radio and television, and infrared radiation from sun?

Each statement that follows refers to a comparison between two radioisotopes, \(A\) and \(X .\) Indicate whether each of the following statements is true or false. (a) If the half-life for \(\mathrm{A}\) is shorter than the half-life for \(\mathrm{X}, \mathrm{A}\) has a larger decay rate constant. (b) If \(X\) is "not radioactive," its half-life is essentially zero. (c) If A has a half-life of 10 yr, and \(X\) has a half-life of $10,000 \mathrm{yr}$, A would be a more suitable radioisotope to measure processes occurring on the 40 -yr time scale.

In 2002 , a team of scientists from Russia and the United States reported the creation of the first atom of element 118 , which is named oganesson, and whose symbol is Og. The synthesis involved the collision of californium- 249 atoms with accelerated ions of an atom which we will denote X. In the synthesis, an oganesson-294 is formed together with three neutrons. $$ { }_{98}^{249} \mathrm{Cf}+\mathrm{X} \longrightarrow{ }_{118}^{294} \mathrm{Og}+3{ }_{0}^{1} \mathrm{n} $$ (a) What are the identities of isotopes X? (b) Isotope \(X\) is unusual in that it is very long-lived (its half-life is on the order of \(10^{19} \mathrm{yr}\) ) in spite of having an unfavorable neutron-to-proton ratio (Figure 21.1). Can you propose a reason for its unusual stability? (c) Oganesson-294 decays into livermorium-290 by alpha decay. Write a balanced equation for this.
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