Question

What particle is produced in each of the following decay reactions? (a) \({ }_{11}^{24} \mathrm{Na} \rightarrow{ }_{12}^{24} \mathrm{Mg}+?\) (b) \({ }_{60}^{135} \mathrm{Nd} \rightarrow{ }_{59}^{135} \mathrm{Pr}+?\) (c) \({ }_{78}^{170} \mathrm{Pt} \rightarrow \frac{166}{76} \mathrm{Os}+?\)

Short answer

(a) Electron and antineutrino, (b) Positron, (c) Alpha particle.

Step-by-step solution

Identify the Reaction Type for Part (a)

The transformation from sodium (Na) to magnesium (Mg) suggests a beta-minus (β-) decay because the atomic number increases by one, indicating the emission of an electron.

Determine the Missing Particle in Part (a)

Since it's a beta-minus decay, the missing particle is an electron (β-) and an antineutrino \(\bar{u}_e\). Thus, the reaction is \[{ }_{11}^{24} \mathrm{Na} \rightarrow { }_{12}^{24} \mathrm{Mg} + \beta^- + \bar{u}_e.\]

Identify the Reaction Type for Part (b)

The conversion from neodymium (Nd) to praseodymium (Pr) involves a decrease in atomic number, typically indicating a beta-plus (β+) decay or electron capture.

Determine the Missing Particle in Part (b)

Given the decrease in atomic number from 60 to 59, this is likely electron capture, where an inner electron is combined with a proton to form a neutron, often emitting an X-ray as a byproduct, or one can consider the emission of a positron (β+).\[{ }_{60}^{135} \mathrm{Nd} \rightarrow { }_{59}^{135} \mathrm{Pr} + \beta^+ + u_e.\]

Identify the Reaction Type for Part (c)

The transformation from platinum (Pt) to osmium (Os) with mass number change from 170 to 166 indicates an alpha (α) decay, as the mass number typically decreases by 4 and atomic number by 2.

Determine the Missing Particle in Part (c)

Alpha decay means that a helium nucleus \(\alpha\) (composed of 2 protons and 2 neutrons) has been emitted. Thus, the reaction is \[{ }_{78}^{170} \mathrm{Pt} \rightarrow { }_{76}^{166} \mathrm{Os} + \alpha.\]

Key concepts

Beta-Minus Decay

In beta-minus decay, also known as \( \beta^- \) decay, a neutron in the nucleus of an atom is transformed into a proton. This process increases the atomic number by one, creating a new element. The neutron change incurs the release of an electron, termed a beta particle, and an antineutrino.The general reaction can be represented as:\[ n \rightarrow p^+ + e^- + \bar{u}_e\]Here, \( n \) represents the neutron, \( p^+ \) is the resulting proton, \( e^- \) is the electron or beta particle, and \( \bar{u}_e \) denotes the antineutrino.Beta-minus decay is vital for the stability of nuclei, helping unstable isotopes achieve equilibrium. Characteristics of this decay include:

• An increase in atomic number by one
• No change in mass number
• Production of an electron and antineutrino

Electron Capture

Electron capture is a process where an inner orbital electron is captured by the nucleus. This electron combines with a proton to form a neutron, lowering the atomic number by one without altering the mass number. Often, this process results in the emission of an X-ray as the atom reorganizes its electron shells.The basic reaction occurring in electron capture is as follows:\[ p^+ + e^- \rightarrow n + u_e\]In this equation, a proton (\( p^+ \)) absorbs an electron (\( e^- \)), converting into a neutron (\( n \)), and a neutrino (\( u_e \)) is released. Key points about electron capture include:

• A decrease in atomic number by one
• Mass number remains unchanged
• Possible emission of an X-ray

Although electron capture changes an element into another by modifying its atomic number, it conserves the overall mass number, balancing the reaction without ejecting particles much like in beta-plus decay.

Alpha Decay

Alpha decay is a type of nuclear decay where an unstable nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons, the same as a helium nucleus. When an atom undergoes alpha decay, its atomic number decreases by two, and its mass number decreases by four.The equation representing alpha decay is typically:\[ X \rightarrow Y + \alpha\]In this equation, \( X \) is the original parent nucleus, \( Y \) is the daughter nucleus formed after the decay, and \( \alpha \) represents the emitted alpha particle.Key insights into alpha decay:

• A decrease in atomic number by two
• A decrease in mass number by four
• Emission of a helium nucleus

Alpha decay commonly occurs in heavier, unstable isotopes as they attempt to reach a more stable configuration. This process effectively modifies the type and energy of the element involved, aiding in the progressive stabilization of high-mass elements.