DP IB Physics: SL

E. Nuclear and Quantum Physics

E.3 Radioactive decay

DP IB Physics: SL E. Nuclear and Quantum Physics E.3 Radioactive decay Guiding questions:
a)	Why are some isotopes more stable than others?
b)	In what ways can a nucleus undergo change?
c)	How do large, unstable nuclei become more stable?
d)	How can the random nature of radioactive decay allow for predictions to be made?

a) Why are some isotopes more stable than others?
Solution:
While the quantity of protons and neutrons in each isotope’s nucleus is balanced, some are more stable than others.
Because stable isotopes have a neutron-to-proton ratio, the nucleus is held together by the strong nuclear force, which overcomes the electrostatic repulsion between protons.
A greater neutron-to-proton ratio is necessary for stability in larger nuclei.
Figure 1 Isotopes of Hydrogen atom
Strong Nuclear Force:
The nucleus is held together by the basic force known as the strong nuclear force, which works between protons and neutrons. The electromagnetic force that makes protons repel one another is far weaker than this force.
Ratio of Neutrons to Protons:
The optimal neutron-to-proton ratio for smaller isotopes is nearly 1:1. More neutrons are required to create a strong enough nuclear force to counterbalance the increasing repulsive attraction between protons in a bigger nucleus.
Decay and Stability:
In order to attain a more stable structure, the nucleus may experience radioactive decay if the neutron-to-proton ratio is not ideal.
Examples include the stable isotope carbon-12, which has six protons and six neutrons. The radioactive isotope carbon-14 has six protons and eight neutrons.
Magical Numbers:
It is suggested that nucleons (protons and neutrons) exist in energy levels or shells similar to electrons in atoms because certain numbers of protons or neutrons (such as 2, 8, 20, 28, 50, 82, and 126) are linked to increased stability.
b) In what ways can a nucleus undergo change?
Solution:
Nuclear processes, which are mainly categorised as nuclear decay (radioactive decay) and nuclear transmutation, can alter a nucleus.
The spontaneous conversion of an unstable nucleus into a more stable one, frequently releasing radiation, is known as nuclear decay.
In contrast, nuclear transmutation is the process by which a nucleus is blasted by particles or other nuclei, creating a new nucleus.
⇒ Nuclear Decay (Radioactive Decay):
Alpha decay:
Alpha decay is the release of an alpha particle (a helium nucleus made up of two protons and two neutrons) by an unstable nucleus. As a result, the nucleus’s mass number drops by 4 and its atomic number drops by 2.
Beta Decay:
A beta particle (an electron or positron) and an antineutrino or neutrino are released when a neutron in the nucleus decays into a proton. The mass number remains unchanged, but the atomic number is altered.
Gamma Decay:
Without altering its composition, an excited nucleus releases energy as high-energy electromagnetic radiation known as gamma rays.
Figure 2 Nuclear decay
⇒ Nuclear transmutation:
Nuclear reaction:
When a nucleus is exposed to a variety of particles, such as protons, neutrons, or other nuclei, it undergoes an induced reaction, which is a non-spontaneous transition into a new nucleus.
Example:
Nuclear transmutation takes happen, for instance, in particle accelerators, nuclear reactors, and the interiors of stars.
c) How do large, unstable nuclei become more stable?
Solution:
Radioactive decay, in which large, unstable nuclei release particles and/or energy to change into a more stable configuration, is how they become stable.
This change frequently entails adjusting the nucleus’s overall composition and energetic state by modifying the amount of protons and/or neutrons within it.
⇒ Neutron – to – Proton ratio:
Neutron-to-proton ratios in stable nuclei typically vary depending on the nucleus’s overall size.
In relation to their proton count, unstable nuclei frequently have either too many or too few neutrons.
This ratio is adjusted with the aid of radioactive decay, which results in a more stable nucleus structure.
Examples include the decay of uranium-238 into a stable isotope of lead via a sequence of alpha and beta decays.
Beta decay transforms carbon-14 into stable nitrogen-14.
⇒ Nuclear Stability:
The binding energy—the energy holding protons and neutrons together—within the nucleus is associated with nuclear stability.
Unstable nuclei are more prone to radioactive decay and have lower binding energies.
Unstable nuclei release energy and change into more stable nuclei with higher binding energies through radioactive decay.
Figure 3 Nuclear stability
d)How can the random nature of radioactive decay allow for predictions to be made?
Solution:
Because radioactive decay is statistical in nature, it is possible to forecast with great precision the behaviour of a large collection of radioactive atoms, but the decay of an individual radioactive atom is fundamentally random and unpredictable.
Although we are unable to identify which individual atoms will decay, we can predict the amount of a radioactive material that will be left after a given amount of time thanks to the decay rate, which is defined by the half-life.
Atomic level randomness:
According to quantum theory, the decay of a single radioactive nucleus is a probabilistic occurrence. No matter how long an atom has existed, it is impossible to predict when it will decay.
Statistical predictability:
The unpredictability evens out when working with a large number of atoms. A radioactive sample’s decay rate is defined by its decay constant, also known as its half-life, which is the probability of decay for the entire sample per unit of time.
Half – life:
The amount of time it takes for half of the radioactive atoms in a sample to decay is known as the half-life. Although we are unable to anticipate the decay of a single atom, this value enables us to estimate the decay rate for a large number of atoms.
Example:
As an illustration, consider tossing a coin. Although it is impossible to anticipate whether the next flip will be heads or tails, you may be quite certain that about half of the flips will be heads and the other half will be tails if you flip the coin a lot.
Similar to this, with radioactive decay, we can predict how many atoms will decay during a specific time period, especially when there are a lot of them, but we cannot predict when a specific atom will decay.
Central limit theorem:
The Central Limit Theorem, which asserts that even in cases where the individual variables are not normally distributed, the average of a large number of independent, identically distributed random variables (such as radioactive decays) will be roughly normally distributed, is connected to the predictability of large numbers of radioactive decays.