Answer to Question #126249 in Atomic and Nuclear Physics for Sammy W-S

Question

1) what type of nuclear decay(s) must occur in a stable isotope to become more stable? explain your choice.
2) what type of nuclear decay must occur in in a unstable isotope to become more stable? Explain your choice.
3) what type of nuclear decay must occur in an isotope with stable nuclides but high atomic numbers and high number of neutrons? Explain your answer.

Answer 1

Atomic nuclei consist of protons and protons, which attract each other through nuclear force while protons repel each other via electric force due to their positive charge. These two forces compete, leading to combinations of neutrons and protons being more stable than others. Neutrons stabilize the nucleus because they attract protons, which helps offset the electrical repulsion between protons. So, as the number of protons increases, an increasing ratio of neutrons is needed to form a stable nucleus; if too many or too few neutrons are present with regard to optimum ratio, nucleus becomes unstable and subject to nuclear decays. Unstable isotopes decay through radioactive decay pathways like alpha decay, beta decay, electron capture or spontaneous fission.

An even number of protons or neutrons is more stable (with high binding energy) because of pairing effects, so even-even nuclides are much more stable than odd-odd nuclides. There are very few stable odd-odd nuclides such that only five are stable, with another four having half-lives longer than a billion years.

Another effect is to prevent beta decay of many even-even nuclides into another even-even nuclide of the same mass number but lower energy because decay proceeding at a pace of one step at a time would have to pass through an odd-odd nuclide of higher energy. (Double beta decay directly from even-even to even-even, skipping over an odd-odd nuclide, is a process so strongly hindered that it has a half-life greater than a billion times the age of the universe). This makes for a larger number of stable even-even nuclides, up to three for some mass numbers and up to seven for few atomic numbers (protons) and minimum four for all stable even-Z elements beyond iron (Fe).

Since a nucleus with an odd number of protons is relatively less stable, odd-numbered elements have fewer stable isotopes. Of the 26 'monoisotopic' elements which have only a single stable isotope, all but one have an odd atomic number - the single exception being Beryllium. No odd-numbered element has more than two stable isotopes while every even-numbered element with stable isotopes, except for helium, carbon and beryllium, has at least three stable isotopes.

1) What type of nuclear decay(s) must occur in a stable isotope to become more stable? 

Explanation:- Alpha decay occurs in massive nuclei which have too large a proton to neutron (p/n) ratio. An alpha particle, with its two protons and two neutrons, is a very stable configuration of particles. Alpha radiation reduces the ratio of protons to neutrons in parent nucleus, bringing it to a more stable configuration. Many nuclei that are more massive than lead (Pb) decay by this method. Consider the example of ²¹⁰Po decaying by emission of an alpha particle. The reaction can be written as: ²¹⁰Po ----> ²⁰⁶Pb + ⁴He

Polonium nucleus has 84 protons and 126 neutrons. The ratio of protons to neutrons is Z/N = 84/126 = 0.667. The ²⁰⁶Pb nucleus has 82 protons and 124 neutrons which gives a ratio of 82/124 = 0.661. This small change in Z/N ratio is enough to put the nucleus into a more stable state and brings 'daughter' nucleus (decay product) into the region of stable nuclei.

Some nuclei spontaneously transform into nuclei with a different number of protons, thereby producing a different element. When it was learnt that these naturally occurring radioactive isotopes decayed by emitting subatomic particles, it was realized that it should be possible to carry out reverse reaction, converting a stable nucleus to another more massive nucleus by bombarding it with subatomic particles in a nuclear transmutation reaction.

In nuclear decay reactions, parent nucleus is converted to a more stable daughter nucleus. Nuclei with too many neutrons decay by converting a neutron to a proton whereas nuclei with too few neutrons decay be converting a proton to a neutron. Very heavy nuclei (with A>200 and Z>83) are unstable and decay by emitting an alpha particle. When an unstable nuclide undergoes radioactive decay, total number of nucleons is conserved as is total positive charge.

Alpha decay results in emission of an alpha particle and produces a daughter nucleus nucleus with a mass number that is lower by 4 and an atomic number that is lower by 2 compared to parent nucleus.

Beta decay converts a neutron to a proton and emits a high-energy electron, producing a daughter nucleus with same mass number as the parent and an atomic number which is higher by 1.

In gamma emission, a daughter nucleus in a nuclear excited state undergoes a transition to a lower-energy state by emitting a gamma ray.

2) What type of nuclear decay must occur in in a unstable isotope to become more stable?

Explanation:- The nuclei of all elements with atomic numbers greater than 83 are unstable. Hence, isotopes of all elements beyond Bismuth in periodic table are radioactive. Because alpha decay decreases Z by only 2 and positron emission or electron capture decreases Z by only 1, it is not possible for a nucleotide with Z>85 to decay into a stable daughter nuclide in a single step, except via nuclear fission. Consequently, radioactive isotopes with Z > 85 often decay to a daughter nucleus that is radioactive, which in turn decays to a second radioactive daughter nucleus, and so on, until a stable nucleus results. This series of sequential alpha and beta-decay reactions is called a radioactive series. Most common is the uranium-238 decay series, which produces lead-206 in a series of 14 sequential alpha and beta-decay reactions.

Though a radioactive decay series can be written for any isotope with Z > 85, only two others occur naturally: decay of uranium-235 to lead-207 (in 11 steps) and Thorium-232 to Lead-208 (in 10 steps). A fourth series, the decay of Neptunium-237 to Bismuth-209 in 11 steps, occurred on primitive Earth.

Due to these radioactive decay series, small amounts of very unstable isotopes are found in ores which contain uranium or thorium. These unstable isotopes should have decayed long ago to stable nuclei with a lower atomic number and they would no longer be found on Earth. Since they are generated continuously by decay of uranium or thorium, their amounts have reached a steady state, in which their rate of formation is equal to their rate of decay. The first of the trans-uranium elements to be prepared was Neptunium (Z=93) which was synthesized by bombarding a 238U target with neutrons. This reaction occurs in two steps. Initially, a neutron combines with a 238U nucleus to form 239U, which is unstable and undergoes beta decay to produce 239Np.

Subsequent beta decay of 239 Np produces the second trans-uranium element, plutonium (Z = 94). Bombarding the target with more massive nuclei creates elements which have atomic numbers greater than that of the target nucleus. Such techniques have resulted in creation of super-heavy elements 114 & 116, both of which lie in or near the 'island of stability'.

⁴⁵Ti₂₂ nuclide has a neuron-to-proton ratio of only 1.05 which is much less than the requirement for stability for an element with an atomic number in this range. Nuclei which have low neutron-to-proton ratios decay by converting a proton to a neutron. Two possibilities are positron emission, which converts a proton to a neutron and a positron and electron capture, which converts a proton and a core electron to a neutron. In this case, both are observed, with positron emission occurring 86% of the time and electron capture around 14% of the time.

¹²B₅ nuclide has a neutron-to-proton ratio of 1:4, which is very high for a high element. Nuclei with high neutron-to-proton ratios decay by converting a neutron to a proton and an electron. Electron is emitted as a beta particle and proton remains in the nucleus, causing increase in atomic number with no change in mass number. So, this nuclide will undergo beta decay.

3) What type of nuclear decay must occur in an isotope with stable nuclides but high atomic numbers and high number of neutrons? 

Explanation:- Beta particles are electrons or positrons (antielectrons). Beta decay occurs when, in a nucleus with too many protons or neutrons, one of the protons or neutrons is transformed into the other. In beta minus decay, a neutron decays into a proton, an electron and an antineutrino. In beta plus decay, a proton decays into a neutron, a positron and a neutrino. Both reactions occur because one or the other will move the product closer to the region of stability. These reactions take place because conservation laws are obeyed. Electric charge conservation requires that if an electrically neutral neutron becomes a positively charged proton, an electrically negative particle (an electron) must also be produced. Similarly, conservation of lepton number requires that if a neutron (lepton number = 0) decays into a proton (lepton number = 0) and an electron (lepton number = 1), a particle with a lepton number of -1 ( antineutrino) must also be produced. Leptons emitted in beta decay did not exist in the nucleus before the decay - they are created at the instant of the decay.

An isolated proton, a hydrogen nucleus with or without an electron, does not decay. But, within a nucleus, the beta decay process can change a proton to a neutron. Isolated neutron is unstable and will decay with a half-life of 10.5 minutes. A neutron in a nucleus will decay if a more stable nucleus results and half-life of decay depends on the isotope. If it leads to a more stable nucleus, a proton in a nucleus may capture an electron from the atom and change into a neutron and a neutrino.

Proton decay, neutron decay and electron capture are three ways in which protons can be changed into neutrons or vice-versa. In each decay, there is a change in atomic number, so that the parent and daughter atoms are different elements. In all the three processes, number A of nucleons remains the same while both proton number (Z) and neutron number (N) increase or decrease by 1.

Some nuclei spontaneously transform into nuclei with a different number of protons, thereby producing a different element. When it was learnt that these naturally occurring radioactive isotopes decayed by emitting subatomic particles, it was realized that it should be possible to carry out reverse reaction, converting a stable nucleus to another more massive nucleus by bombarding it with subatomic particles in a nuclear transmutation reaction.

Very heavy nuclei with high neutron-to-proton ratios can undergo spontaneous fission, in which the nucleus breaks into two pieces which can have different atomic numbers and atomic masses with release of neutrons. Very heavy nuclei decay via a radioactive decay series - a succession of alpha- and beta-decay reactions.

In nuclear transmutation reactions, a target nucleus is bombarded with energetic subatomic particles to give a product nucleus which is more massive than the original. All trans-uranium elements with Z > 92 are artificial and must be prepared by nuclear transmutation reactions.

²⁵⁶Fm₁₀₀ is a massive nuclide, with an atomic number of 100 and a mass number greater than 200. Nuclides with A>200 tend to decay by alpha emission and even heavier nuclei tend to undergo spontaneous fission. Thus, the given nuclide will decay by either or both of these two processes. Factually, it decays by both spontaneous fission and alpha emission, in a 97:3 ratio.