Neutrons-to-protons ratio

Estimate the optimal number of neutrons for a nucleus containing 70 protons. 

The type of radioactive decay that a particular radionuclide undergoes depends largely on how its neutron-to-proton ratio compares with those of nearby nuclei that lie within the belt of stability. We can envision three general situations  

Nuclei above the belt of stability (high neutron-to-proton ratios). These neutron-rich nuclei can lower their ratio and thereby move toward the belt of stability by emitting a beta particle because beta emission decreases the number of neutrons and increases the number of protons (Equation 21.3). 

Nuclei with atomic numbers S84. These heavy nuclei tend to undergo alpha emission, which decreases both the number of neutrons and the number of protons by two, moving the nucleus diagonally toward the belt of stability. 

The dark blue dots in HGU RE 21.2 represent stable (nonradioactive) isotopes. The region of the graph covered by these dark blue dots is known as the belt cf stability. The belt of stability ends at element 83 (bismuth), which means that all nudei widi 84 or more protons are radioactive. For example, all isotopes of uranium, Z = 92, are radioactive. 

Nucleibdowtbe belt of stability (lowneutron-to-proton ratios). These proton-rich nuclei can increase their ratio and so move closer to the belt of stability by either positron emission or electron capture because both decays increase the number of neutrons and decrease the number of protons (Equations 21.5 and 21.7). Positron emission is more common among lighter nuclei. Electron capture becomes increasingly common as the nuclear charge increases. 

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An alplia p uticle is an energetic helium nucleus. The alplia particle is released from a radioactive element witli a neutron to proton ratio tliat is too low. The helium nucleus consists of two protons and two neutrons. The alplia particle differs from a helimn atom in that it is emitted witliout any electrons. The resulting daughter product from tliis tj pe of transformation lias an atomic number Uiat is two less tluin its parent and an atomic mass number tliat is four less. Below is an e. aiiiple of alpha decay using polonium (Po) polonium has an atomic mass number of 210 (protons and neutrons) and atomic number of 84. 

Similar to beta decay is positron emission, where tlie parent emits a positively cliargcd electron. Positron emission is commonly called betapositive decay. Tliis decay scheme occurs when tlie neutron to proton ratio is too low and alpha emission is not energetically possible. Tlie positively charged electron, or positron, will travel at higli speeds until it interacts with an electron. Upon contact, each of tlie particles will disappear and two gamma rays will... 

Whether or not a given nucleus will be stable depends on its neutron-to-proton ratio. The 264 known stable nuclei, shown as red dots in Figure 2.5 (page 30), fall within a relatively... 

As you can see from Figure 2.5, the neutron-to-proton ratio required for stability varies with atomic number. For light elements (Z < 20), this ratio is close to 1. For example, the isotopes C, N, and are stable. As atomic number increases, the ratio increases the belt of stability shifts to higher numbers of neutrons. With very heavy isotopes such as 2j Pb, the stable neutron-to-proton ratio is about 1.5 ... 

The stable neutron-to-proton ratio near the middle of the periodic table, where the fission products are located, is considerably smaller (—1-2) than that of uranium-235 (1.6). Hence the immediate products of the fission process contain too many neutrons for stability ... 

Neutron-to-proton ratio, 29-30 Newton, 457,635 Newton, Isaac, 136 Nickel hydroxide, 78 Nicotinic acid, 364-365 NIMBY syndrome, 526 Nitric acid acid rain and, 400 acid strength of, 567 commercial use, 76 copper penny dissolving in, 570 production, 570-571... 

Actinium-225 decays by successive emission of three u particles, (a) Write the nuclear equations for the three decay processes, (b) Compare the neutron-to-proton ratio of the final daughter product with that of actinium-225. Which is closer to the band of stability ... 

A sample of polonium (Po) spontaneously decays into lead (Pl>). The neutron-to-proton ratio of the polonium before it began to decay was —... 

The magic numbers which impart stability to a nucleus are 2, 8, 20, 28, 50, 82 or 122. The isotope, 39K, has a magic number equal to its number of neutrons, so it is probably stable. The others have a larger neutron-to-proton ratio, making them neutron-rich nuclei, so 40K and 41K might be expected to decay by beta emission. In fact, both 39K and 41K are stable, and 40K does decay by beta emission. 

For a given mass number there is a known, stable neutron to proton ratio which varies from 1 to 1.5 as the mass increases (Figure 10.2). Any nucleide whose ratio falls outside of these values will be unstable and decay so as to obtain a more stable ratio. In doing so, it will interconvert neutrons and protons and... 

Know that nuclear stability is best related to the neutron-to-proton ratio (n/p), which starts at about 1/1 for light isotopes and ends at about 1.5/1 for heavier isotopes with atomic numbers up to 83- All isotopes of atomic number greater than 84 are unstable and will commonly undergo alpha decay. Below atomic number 84, neutron-poor isotopes will probably undergo positron emission or electron capture, while neutron-rich isotopes will probably undergo beta emission. 

The stability of the atomic nucleus depends upon a critical balance between the repulsive and attractive forces involving the protons and neutrons. For the lighter elements, a neutron to proton ratio (N P) of about 1 1 is required for the nucleus to be stable but with increasing atomic mass, the N P ratio for a stable nucleus rises to a value of approximately 1.5 1. A nucleus whose N P ratio differs significantly from these values will undergo a nuclear reaction in order to restore the ratio and the element is said to be radioactive. There is, however, a maximum size above which any nucleus is unstable and most elements with atomic numbers greater than 82 are radioactive. 

The stability of nuclides is characterized by several important rules, two of which are briefly discussed here. The first is the so-called synunetry rule, which states that in a stable nuclide with low atomic number, the number of protons is approximately equal to the number of neutrons, or the neutron-to-proton ratio, N/Z, is approximately equal to unity. In stable nuclei with more than 20 protons or neutrons, the N/Z ratio is always greater than unity, with a maximum value of about 1.5 for the heaviest stable nuclei. The electrostatic Coulomb repulsion of the positively charged protons grows rapidly with increasing Z. To maintain the stability in the nuclei, more... 

In the case of rapid capture, several neutrons are added before conversions of type n p bring the neutron to proton ratio back to reasonable proportions. The r process requires impressive neutron fluxes and extreme densities and temperatures that can only be achieved in type II supernovas or the coalescence of two neutron stars. The details are not yet understood. However, we have no other explanation for the existence of gold and heavy isotopes of tin ( Sn and " Sn), for example. There is another process, namely photodisintegration, which is very short-lasting and leads to nuclei poor in neutrons, or rich in protons (referred to as a p process). 

RADIOACTIVE DECAY. Many atomic nuclei have unstable neutron-to-proton ratios and undergo spontaneous first-order decay through the emission of a, I3, or (3 particles or gamma rays. 

B) Carbon-14 has 6 protons and 8 neutrons giving a neutron-to-proton ratio of 1.3 1. Elements with low atomic numbers normally have stable nuclei with approximately equal numbers of neutrons and protons. Thus, C-14 with a high neutron-to-proton ratio results in the emission of a beta particle (high speed electron) ... 

Beta particle emission results in the lowering of the neutron-to-proton ratio. 

Make an estimate of the neutron-to-proton ratio in the center of the sun if the only source of neutrons is thermal equilibrium of the weak interactions. 

Why does /3 decay occur Well, stable nuclei have stable ratios between the proton number and neutron number. These ratios are nontrivial to predict, and are arcane to the extent that they include the concept of magic numbers. 1 Beta-minus emission occurs because some nuclei have too many neutrons therefore /3 decay is energetically favorable, resulting in a reduction in the neutron-to-proton ratio. 

Electron Capture Decay. Electron capture decay is a competing process to positron decay and thus results in an increase in the neutron-to-proton ratio in the nucleus. In this process, a bound, inner orbital electron is captured by the nucleus, resulting in the conversion of a proton into a neutron, the emission of a neutrino, and, if the daughter nucleus is left in an excited state, the emission of one or more gamma rays. The net reaction is shown below ... 

The main factor in determining whether a nucleus will decay is the neutron to proton ratio. Stable atoms have a neutron to proton ratio close to 1. The ratio in unstable atoms is greater than 1. Nature likes a balance between the neutrons and the protons, so the nuclei give off radioactivity in the form of alpha or beta particles in an attempt to bring the neutron to proton ratio closer to 1. 

Thorium-234 has 90 protons and 144 neutrons for a neutron to proton ratio greater than 1 (144 /90). Thorium-234 emits a beta particle. This particle is given off when a neutron breaks into a proton and an electron. The proton stays in the nucleus changing it to 91 protons which is Protactinium -234 while emitting the electron as a beta particle. 

No, this one-to-one neutron-to-proton ratio is outside the belt of stability. Ni-58 yes (p = 28 n = 30 both even)... 

Q Atoms whose nuclei are above the band of stability (high neutron-to-proton ratio) can lower their numbers of neutrons by undergoing beta emissions. The typical pattern for these is that the mass number (number of neutrons + number of protons) is greater than the atomic weight. Remember that beta emissions convert neutrons into protons and beta particles. 

Tritium is hydrogen of mass number 3, having two neutrons and a proton in its nucleus. It is radioactive (half-life 12.4 years) in common with many isotopes having a large neutron-to-proton ratio, tritium decays with emission of an electron (called a beta ray). Such a decay can be represented by the nuclear equation (see also Chap. 27) ... 

Te 5.10 alpha particles and 5 beta particles 7. Refer to Table 21.2 for potential radioactive decay processes. 17F and, 8F contain too many protons or too few neutrons. Electron capture or positron production are both possible decay mechanisms that increase the neu-tron-to-proton ratio. Alpha-particle production also increases the neu-tron-to-proton ratio, but it is not likely for these light nuclei. 21F contains too many neutrons or too few protons. Beta-particle production lowers the neutron-to-proton ratio, so we expect 21F to be a /3-emitter. 9. a. 2gCf + gO - fcIJSg + 4jn b. Rf 11. 6.35 X 1011 13. a. 

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