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Chapter 19: Problem 63

Predict whether each of the following nuclides is stable or unstable (radioactive). If the nuclide is unstable, predict the type of radioactivity you would expect it to exhibit. a. \({ }_{19} \mathrm{~K}\) b. \({ }_{26}^{56} \mathrm{Fe}\) c. \({ }_{11}^{20} \mathrm{Na}\) d. \({ }_{81}^{194} \mathrm{Tl}\)

Short Answer

Expert verified
a. Cannot predict stability and decay type without a given mass number. b. \({ }_{26}^{56} \mathrm{Fe}\) is stable. c. \({ }_{11}^{20} \mathrm{Na}\) is unstable and undergoes beta-minus decay. d. \({ }_{81}^{194} \mathrm{Tl}\) is unstable and undergoes beta-minus decay.

Step by step solution

01

Identify the number of neutrons and protons

The element is Potassium (K) with 19 protons.
02

Calculate the neutron-to-proton ratio

Since there are 19 protons, the neutron to proton ratio will be approximately 1:1, hence we expect 19 neutrons.
03

Determine stability and decay type

Given that there is only the atomic number and no mass number provided, we cannot predict a specific nuclide's stability or decay type in this case. b. \({ }_{26}^{56} \mathrm{Fe}\)
04

Identify the number of neutrons and protons

For \({ }_{26}^{56} \mathrm{Fe}\), there are 26 protons and (56-26) = 30 neutrons.
05

Calculate the neutron-to-proton ratio

The neutron-to-proton ratio is 30:26, approximately 1.15:1.
06

Determine stability and decay type

Iron-56 is stable as it is lighter than the maximum stability line (Z < 20), and its neutron-to-proton ratio is close to 1:1. c. \({ }_{11}^{20} \mathrm{Na}\)
07

Identify the number of neutrons and protons

The nuclide has 11 protons and (20-11) = 9 neutrons.
08

Calculate the neutron-to-proton ratio

The neutron-to-proton ratio is 9:11, or approximately 0.82:1.
09

Determine stability and decay type

Sodium-20 is unstable, given its N:Z ratio falls on the low side of the curve. It will undergo beta-minus decay, as there are more protons than desired, and a neutron will be converted to a proton. d. \({ }_{81}^{194} \mathrm{Tl}\)
10

Identify the number of neutrons and protons

The nuclide has 81 protons and 194 - 81 = 113 neutrons.
11

Calculate the neutron-to-proton ratio

The neutron-to-proton ratio is 113:81, or approximately 1.39:1.
12

Determine stability and decay type

This nuclide is unstable. Due to its high proton number, it is likely to undergo beta-minus decay.

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Most popular questions from this chapter

Why are the observed energy changes for nuclear processes so much larger than the energy changes for chemical and physical processes?

A recently reported synthesis of the transuranium element bohrium (Bh) involved the bombardment of berkelium-249 with neon-22 to produce bohrium-267. Write a nuclear reaction for this synthesis. The half-life of bohrium-267 is \(15.0\) seconds. If 199 atoms of bohrium- 267 could be synthesized, how much time would elapse before only 11 atoms of bohrium- 267 remain? What is the expected electron configuration of elemental bohrium?

When using a Geiger-Müller counter to measure radioactivity, it is necessary to maintain the same geometrical orientation between the sample and the Geiger-Müller tube to compare different measurements. Why?

Technetium-99 has been used as a radiographic agent in bone scans \(\left({ }_{4,}^{99} \mathrm{Tc}\right.\) is absorbed by bones). If \({ }_{43}^{99} \mathrm{Tc}\) has a half-life of \(6.0\) hours, what fraction of an administered dose of \(100 . \mu \mathrm{g}_{43}^{99} \mathrm{Tc}\) remains in a patient's body after \(2.0\) days?

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. \({ }^{3} \mathrm{H}(\beta)\) b. \({ }_{3}^{8} \mathrm{Li}(\beta\) followed by \(\alpha\) ) c. \({ }_{4}^{7} \mathrm{Be}\) (electron capture) d. \({ }_{5}^{8} \mathrm{~B}\) (positron)
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