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Chapter 21: Problem 96

Francium-223 is a radioactive alkali metal that decays by beta emission. Write the nuclear equation for this decay process.

Short Answer

Expert verified
The nuclear equation is \( ^{223}_{87}Fr \rightarrow ^{223}_{88}Ra + ^{0}_{-1}e + \overline{\nu}_e \).

Step by step solution

01

Identify the Initial Element

Francium-223 is the element that undergoes decay. It is represented as \( ^{223}_{87}Fr \), where 223 is the mass number and 87 is the atomic number of Francium.
02

Understand Beta Decay

Beta decay involves the transformation of a neutron into a proton, accompanied by the emission of a beta particle (an electron, \( ^{0}_{-1}e \)). This increases the atomic number by 1 while the mass number remains unchanged.
03

Determine the Element After Decay

After a beta decay, the atomic number of Francium increases by 1, changing it from 87 to 88. The mass number remains at 223, resulting in the formation of Radium, represented as \( ^{223}_{88}Ra \).
04

Write the Nuclear Equation

The nuclear equation for the beta decay of Francium-223 is written as follows: \[ ^{223}_{87}Fr \rightarrow ^{223}_{88}Ra + ^{0}_{-1}e + \overline{u}_e \] where \( ^{0}_{-1}e \) is the beta particle and \( \overline{u}_e \) is the antineutrino, which is often emitted along with the beta particle.

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Key Concepts

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

Understanding Beta Decay
Beta decay is a fascinating process that occurs in certain unstable atomic nuclei. It involves the transformation of a neutron into a proton within the nucleus of an atom. This process is accompanied by the emission of a beta particle and an antineutrino.
  • The beta particle is essentially an electron, denoted as \(^0_{-1}e\).
  • Beta decay increases the atomic number by 1 but leaves the mass number unchanged.
  • The emission of an antineutrino (\(\overline{u}_e\)) helps to conserve energy and angular momentum in the decay process.
To illustrate, when Francium-223 undergoes beta decay, a neutron turns into a proton, thus changing Francium into Radium. The equation for this transformation is:\[ ^{223}_{87}Fr \rightarrow ^{223}_{88}Ra + ^{0}_{-1}e + \overline{u}_e \]This highlights how unstable isotopes reach more stable forms through beta decay.
Exploring Radioactive Decay
Radioactive decay is the natural process by which an unstable atomic nucleus loses energy by emitting radiation. It is one way unstable atoms achieve stability. There are several types of radioactive decay, with beta decay being one of them.
  • Radioactive decay can occur in elements with naturally unstable nuclei.
  • This instability often results from an imbalance in the number of protons and neutrons.
  • Decay leads to the emission of particles like alpha particles, beta particles, neutrons, or gamma rays.
Over time, through decay, a radioactive element may change into a completely different element. In Francium-223's case, through beta decay, it transforms into Radium. This alteration in the atomic structure happens naturally and consistently helps scientists study and understand atomic behavior.
Alkali Metals and Their Properties
Alkali metals like Francium are found in Group 1 of the periodic table. These metals are known for their highly reactive properties due to the presence of a single electron in their outermost shell.
  • Alkali metals include Lithium, Sodium, Potassium, Rubidium, Cesium, and Francium.
  • These elements have low melting points and are typically soft.
  • Due to their reactivity, they are never found in nature in their elemental form.
Francium is unique as it is highly radioactive and decays into other elements through processes like beta decay, making it one of the rarest under studied alkali metals. Understanding the properties of alkali metals helps humans harness their potential in various applications, from chemistry to industrial processes.

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