Beta Decay Flashcards

Beta Decay

• Beta decay involves an unstable nucleus seeking stability due to an imbalance in the strong force.

• The nucleus contains protons and neutrons.

The Process of Beta Decay

• A neutron transforms into a proton and an electron.

• This transformation can be represented as: neutron → proton + electron

• The equation is balanced in terms of charge: a neutron (neutral charge) becomes a proton (positive charge) and an electron (negative charge), thus maintaining charge neutrality ( +1 charge + -1 charge = 0 charge).

• Electrons have negligible mass compared to protons (approximately $10,000$$$10,000$$ times less massive).

• The mass difference between a neutron and a proton is essentially the mass of an electron; therefore, a neutron can be considered as a combination of a proton and an electron.

Beta Particle

• In beta decay, one of the neutrons transforms into a proton and an electron, and this electron is emitted as radiation.

• This emitted electron is called a beta particle.

• Every beta particle is an electron (denoted as $e$$$e$$).

• In contrast, an alpha particle is a helium nucleus ($He$$$He$$), specifically $^{4}_{2}He$$$^{4}_{2}He$$.

Example: Carbon-14 Beta Decay

• Carbon-14 ($^{14}C$$$^{14}C$$) is radioactive and undergoes beta decay.

• Carbon has 6 protons, so the full notation is $^{14}_{6}C$$$^{14}_{6}C$$.

• The beta decay equation: $$^{14}{6}C \rightarrow \, ^{A}{Z}X + \, ^{0}_{-1}e$$ Where:

  • $^{14}_{6}C$$$^{14}_{6}C$$ is the parent nucleus (Carbon-14).

  • $^{A}_{Z}X$$$^{A}_{Z}X$$ is the daughter nucleus (the new element formed after decay).

  • $^{0}_{-1}e$$$^{0}_{-1}e$$ is the beta particle (electron).

• During beta decay:

  • The number of neutrons decreases by one.

  • The number of protons increases by one.

  • The total number of nucleons (protons + neutrons) remains the same.

• In the example, Carbon-14 decays into Nitrogen-14 ($^{14}N$$$^{14}N$$):
  $$^{14}{6}C \rightarrow \, ^{14}{7}N + \, ^{0}_{-1}e$$

• The atomic number (number of protons) increases by one (6 to 7), changing the element from carbon to nitrogen.

Balancing Beta Decay Equations

• The beta particle is represented as $^{0}_{-1}e$$$^{0}_{-1}e$$.

• The mass number (A) remains constant during beta decay.

• The atomic number (Z) increases by one during beta decay.

• To balance the equation, ensure that the sums of mass numbers and atomic numbers are equal on both sides.

• Use the periodic table to identify the element based on its atomic number.

  • In the example: $$^{A}{Z}X + \, ^{0}{-1}e = \, ^{14}_{6}C $$, therefore A = 14 and Z = 7. Element number 7 is Nitrogen (N).

Key Points to Remember

• Alpha particle: Always $^{4}_{2}He$$$^{4}_{2}He$$.

• Beta particle: Always $^{0}_{-1}e$$$^{0}_{-1}e$$.

• Knowing these, along with a periodic table, allows one to balance beta decay equations.

Other Types of Decay

• Some elements undergo both alpha and beta decay.

• Example: Uranium-238 decays via alpha decay into Thorium, which then undergoes both alpha and beta decay in a decay chain eventually leading to lead.

Inverse Beta Decay and Neutron Stars

• The reverse process (electron + proton → neutron) occurs in neutron stars.

• Neutron Star Formation:

  • Stars with 8-25 solar masses explode, compressing the core.

  • Electrons are forced into protons, creating neutrons.

  • The core collapses into a ball of neutrons, forming a neutron star.

Application

• Sodium-29 also undergoes beta decay.

Homework

• Write equations for beta decay processes.