Problem 57 - Introductory Chemistry Atoms First

Question

What happens when an atom's nucleus undergoes: (a) positron emission. (b) electron capture. (c) gamma emission.

Step-by-Step Solution

Answer

When an atom's nucleus undergoes (a) positron emission, a proton in the nucleus converts into a neutron and releases a positron and an electron neutrino, resulting in a new element with an atomic number decreased by one. (b) In electron capture, a nucleus absorbs an inner shell electron, converting a proton into a neutron and releasing an electron neutrino, forming a new element with an atomic number decreased by one and emitting an X-ray or Auger electron. (c) During gamma emission, an excited nucleus releases excess energy as a gamma-ray photon to return to a lower energy state, without any change in the atomic or mass number of the element.

Step 1: (a) Positron Emission)

Positron emission is a type of radioactive decay in which the nucleus of an atom releases a positron (a positively charged particle with the same mass as an electron). This process occurs when a proton in the nucleus converts into a neutron, releasing a positron and a neutrino. Step 1: Proton conversion in the nucleus The nucleus of the atom contains protons and neutrons. When a proton in the nucleus is converted into a neutron, it releases a positron (β+) and an electron neutrino (νe). Step 2: Positron emission The released positron is then emitted from the nucleus, resulting in a decrease in the atomic number (Z) of the element by one, while the mass number (A) remains the same. Step 3: The new element As a result of the reduced atomic number, a new element is formed. For example, if carbon-11 undergoes positron emission, it becomes boron-11.

Step 2: (b) Electron Capture)

Electron capture is another type of radioactive decay in which a nucleus absorbs an inner shell electron. This process occurs when a proton in the nucleus captures an electron and converts into a neutron, releasing an electron neutrino (νe). Step 1: Electron capture in the nucleus An inner shell electron is drawn into the atom's nucleus, combining with a proton to form a neutron. The electron is usually from the K or L shell. Step 2: Formation of a new element As a result of the captured electron, the atomic number (Z) of the element decreases by one, while the mass number (A) remains the same. Step 3: X-ray or Auger electron emission After the electron is captured, a vacancy is created in the electron shell. An electron from a higher energy level falls into this vacancy, releasing an X-ray or an Auger electron (another electron) to conserve energy.

Step 3: (c) Gamma Emission)

Gamma emission is a type of radioactive decay in which an atom's nucleus releases excess energy in the form of gamma rays (high-energy photons). This process occurs when an excited nucleus returns to a lower energy state. Step 1: Nuclear excitation The nucleus of an atom is in an excited state when it has more energy than its ground state (lowest possible energy level). This excess energy can be due to a preceding nuclear decay process such as alpha or beta decay. Step 2: Gamma-ray emission To return to a lower energy state, the nucleus releases energy in the form of a photon, known as a gamma-ray (γ). This process is similar to an electron transitioning to a lower energy level and emitting a photon in atomic excitations but involves the nucleus instead of electrons. Step 3: Stable or less excited nucleus After the gamma emission, the nucleus is either in its ground state or a less excited state. This process does not change the atomic number (Z) or the mass number (A) of the atom, so the resulting element remains the same.

Key Concepts

Positron Emission

Positron emission represents an intriguing facet of nuclear physics, where balance within the atom's nucleus shifts in a bid to achieve stability. Here's a closer look:

In nature's quest for balance, a proton within the nucleus undergoes transformation into a neutron. This process isn't as simple as a change of identity; it's a matter of particle exchange. The proton sheds its positive charge in the form of a positron (denoted as \( \beta^+ \)), which is an antiparticle of the electron, carrying the same mass but with a positive charge. Accompanying the positron, a subtle particle called an electron neutrino (denoted as \( u_e \) ) is also released.

The emission of the positron effectively decreases the atomic number (noted as \( Z \) ) by one, yet the mass number (notated as \( A \) ) remains untouched. To visualize this, picture carbon-11; one of its protons decides to become a neutron, leading to positron emission and the formation of boron-11. While the mass is constant, the fundamental nature of the element shifts — a transformation from one element to another.

Electron Capture

Less like an emission and more of an intimate merger, electron capture is an alternate decay route where the nucleus draws in one of its own. This close encounter of a subatomic kind has significant consequences:

Within the heart of the atom, a proton reaches out and captures an inner shell electron, usually from the K or L shell. This extraordinary internal interaction results in the fusion of the proton and electron into a neutron. An electron neutrino, a byproduct of the process, silently slips away from the nucleus.

With the atomic number (\( Z \) ) reduced by one, yet the mass number (\( A \) ) preserved, the atom morphs into a new element. The absence of the captured electron leaves a vacancy that triggers a cascade within the electron shells. An electron from a higher shell falls to fill the void, emitting energy in the guise of an X-ray or, alternatively, an Auger electron — a sophisticated energy-balancing act.

Gamma Emission

Gamma emission is nature's way of calming an overexcited atomic nucleus. Think of it as the nucleus taking a deep breath and relaxing, releasing a burst of energy as it settles:

An atomic nucleus, agitated and brimming with surplus energy, seeks a return to tranquility, its ground state. This excess energy often follows a nuclear decay process such as alpha or beta decay. The pathway back to a serene state involves emitting a photon far more energetic than any part of visible light — a gamma-ray (denoted as \( \gamma \)).

This phenomenon doesn't involve the electron cloud surrounding the nucleus but engages the nucleus itself, distinguishing it from typical atomic emissions. What comes after the gamma flash is a nucleus that's either found its peace in the ground state or, at the very least, stepped down to a lesser degree of excitement. Importantly, this radioactive release doesn't alter the atomic number (\( Z \) ) or mass number (\( A \) ), leaving the element's identity intact. It's an atomic adjustment internal to the nucleus, a shift from a higher to a lower energy level without a change in form.