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Chapter 21: Problem 11

Write balanced nuclear equations for the following processes: (a) rubidium-90 undergoes beta decay; (b) selenium-72 undergoes electron capture; (c) krypton-76 undergoes positron emission; (d) radium-226 emits alpha radiation.

Short Answer

Expert verified
The short answer version of the balanced nuclear equations for the given processes are as follows: a) Rubidium-90 undergoing beta decay: \(^{90}_{37}\textrm{Rb} \rightarrow ^{90}_{38}\textrm{Sr} + ^0_{-1}\beta\) b) Selenium-72 undergoing electron capture: \(^{72}_{34}\textrm{Se} + ^0_{-1}e \rightarrow ^{72}_{33}\textrm{As}\) c) Krypton-76 undergoing positron emission: \(^{76}_{36}\textrm{Kr} \rightarrow ^{76}_{35}\textrm{Br} + ^0_{+1}e\) d) Radium-226 emitting alpha radiation: \(^{226}_{88}\textrm{Ra} \rightarrow ^{222}_{86}\textrm{Rn} + ^4_2\alpha\)

Step by step solution

01

a) Rubidium-90 undergoes beta decay

In beta decay, a neutron is converted into a proton, and an electron (beta particle) is emitted. The atomic number (number of protons) increases by 1, while the mass number (number of protons + number of neutrons) remains the same. The balanced nuclear equation for beta decay of rubidium-90 (Rb-90) is: \(^{90}_{37}\textrm{Rb} \rightarrow ^{90}_{38}\textrm{Sr} + ^0_{-1}\beta\)
02

b) Selenium-72 undergoes electron capture

In electron capture, a proton inside the nucleus captures an electron and is converted into a neutron. The atomic number (number of protons) decreases by 1, while the mass number (number of protons + number of neutrons) remains the same. The balanced nuclear equation for electron capture of selenium-72 (Se-72) is: \(^{72}_{34}\textrm{Se} + ^0_{-1}e \rightarrow ^{72}_{33}\textrm{As}\)
03

c) Krypton-76 undergoes positron emission

In positron emission, a proton is converted into a neutron and a positron is emitted. The atomic number (number of protons) decreases by 1, while the mass number (number of protons + number of neutrons) remains the same. The balanced nuclear equation for positron emission of krypton-76 (Kr-76) is: \(^{76}_{36}\textrm{Kr} \rightarrow ^{76}_{35}\textrm{Br} + ^0_{+1}e\)
04

d) Radium-226 emits alpha radiation

In alpha decay, an alpha particle (composed of two protons and two neutrons) is emitted from the nucleus. The atomic number (number of protons) decreases by 2, and the mass number (number of protons + number of neutrons) decreases by 4. The balanced nuclear equation for alpha decay of radium-226 (Ra-226) is: \(^{226}_{88}\textrm{Ra} \rightarrow ^{222}_{86}\textrm{Rn} + ^4_2\alpha\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Beta Decay
Beta decay is a type of radioactive decay where an unstable nucleus emits a beta particle. This beta particle is an electron. During beta decay, a neutron in the nucleus is transformed into a proton. This change increases the atomic number by one, while the mass number remains unchanged. Let's take the example of rubidium-90. When it undergoes beta decay, it turns into strontium-90.
The nuclear equation can be written as:
  • Rubidium-90: \(^{90}_{37}\text{Rb} \rightarrow ^{90}_{38}\text{Sr} + ^0_{-1}\beta\)
This process changes the element to the next one on the periodic table, but with the same mass number. This transformation is essential in nuclear reactions and is one way elements can change into other elements in nature.
Electron Capture
Electron capture occurs when an inner orbital electron is captured by the nucleus. Inside the nucleus, this electron combines with a proton to form a neutron. As a result, the atomic number decreases by one, while the mass number remains constant.
For selenium-72, during electron capture, it is transformed into arsenic-72. The nuclear equation illustrates this process:
  • Selenium-72:\(^{72}_{34}\text{Se} + ^0_{-1}e \rightarrow ^{72}_{33}\text{As}\)
Electron capture is unique because it involves an existing atomic orbital electron, typically a characteristic of elements with higher atomic numbers. This mechanism helps stabilize the nucleus by altering its proton-to-neutron ratio.
Positron Emission
In positron emission, a proton in the nucleus is converted into a neutron, emitting a positron. A positron is the antimatter counterpart of an electron, having the same mass but a positive charge.
This causes the atomic number to decrease by one, while the mass number remains unchanged. For krypton-76, positron emission changes it to bromine-76:
  • Krypton-76:\(^{76}_{36}\text{Kr} \rightarrow ^{76}_{35}\text{Br} + ^0_{+1}e\)
Positron emission helps us understand processes in a nuclear reactor and even in medical applications like PET scans. It's an important nuclear process used for transforming and stabilizing nuclei.
Alpha Decay
Alpha decay is a form of radioactive decay where an atomic nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons, resembling a helium nucleus. When a nucleus undergoes alpha decay, its atomic number decreases by two, and its mass number decreases by four.
In the case of radium-226, alpha decay results in the formation of radon-222:
  • Radium-226:\(^{226}_{88}\text{Ra} \rightarrow ^{222}_{86}\text{Rn} + ^4_2\alpha\)
Alpha decay is a common process in heavier elements, allowing them to release energy and become more stable. Understanding this process is key in fields such as geology, where alpha decay can be used for dating rocks and fossils.

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Most popular questions from this chapter

Write balanced nuclear equations for the following transformations: (a) gold-191 undergoes electron capture; (b) gold-201 decays to a mercury isotope; (c) gold198 undergoes beta decay; (d) gold-188 decays by positron emission.

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a halflife of \(8.02\) days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive. (a) Why is Nal a good choice for the source of iodine? (b) If a Geiger counter is placed near the person's thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time? (c) A normal thyroid will take up about \(12 \%\) of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to \(0.01 \%\) of the original amount?

The half-life for the process \({ }^{238} \mathrm{U} \longrightarrow{ }^{206} \mathrm{~Pb}\) is \(4.5 \times 10^{9}\) yr. A mineral sample contains \(75.0 \mathrm{mg}\) of \({ }^{238} \mathrm{U}\) and \(18.0 \mathrm{mg}\) of \(^{206} \mathrm{~Pb}\). What is the age of the mineral?

Predict the type of radioactive decay process for the following radionuclides: (a) \({ }_{5}^{8} \mathrm{~B}\), (b) \({ }_{29}^{68} \mathrm{Cu}\), (c) phosphorus32, (d) chlorine-39.

Using the concept of magic numbers, explain why alpha emission is relatively common, but proton emission is nonexistent.
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