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The fact that nuclear forces are very strong is responsible for the very large energies emitted in nuclear decay. During decay, the forces do work, and since work is force times the distance, a large force can result in a large emitted energy. In fact, we know that there are two distinct nuclear forces because of the different types of nuclear decay—the strong nuclear force is responsible for α size 12{α} {} decay, while the weak nuclear force is responsible for β size 12{β} {} decay.

The many stable and unstable nuclei we have explored, and the hundreds we have not discussed, can be arranged in a table called the chart of the nuclides    , a simplified version of which is shown in [link] . Nuclides are located on a plot of N size 12{N} {} versus Z size 12{Z} {} . Examination of a detailed chart of the nuclides reveals patterns in the characteristics of nuclei, such as stability, abundance, and types of decay, analogous to but more complex than the systematics in the periodic table of the elements.

A chart of nuclides is shown with x axis labeled as number of protons or atomic number with range zero to one hundred ten and y axis labeled as number of neutrons with range zero to one hundred sixty. A straight dashed line is shown for equal atomic number and number of nuclides. A number of points are plotted above the dashed line. The region up to atomic number eighty and neutron number one hundred thirty is shown as stable nuclei and above this region is unstable nuclei.
Simplified chart of the nuclides, a graph of N size 12{N} {} versus Z size 12{Z} {} for known nuclides. The patterns of stable and unstable nuclides reveal characteristics of the nuclear forces. The dashed line is for N = Z size 12{N=Z} {} . Numbers along diagonals are mass numbers A size 12{A} {} .

In principle, a nucleus can have any combination of protons and neutrons, but [link] shows a definite pattern for those that are stable. For low-mass nuclei, there is a strong tendency for N size 12{N} {} and Z size 12{Z} {} to be nearly equal. This means that the nuclear force is more attractive when N = Z size 12{N=Z} {} . More detailed examination reveals greater stability when N size 12{N} {} and Z size 12{Z} {} are even numbers—nuclear forces are more attractive when neutrons and protons are in pairs. For increasingly higher masses, there are progressively more neutrons than protons in stable nuclei. This is due to the ever-growing repulsion between protons. Since nuclear forces are short ranged, and the Coulomb force is long ranged, an excess of neutrons keeps the protons a little farther apart, reducing Coulomb repulsion. Decay modes of nuclides out of the region of stability consistently produce nuclides closer to the region of stability. There are more stable nuclei having certain numbers of protons and neutrons, called magic numbers    . Magic numbers indicate a shell structure for the nucleus in which closed shells are more stable. Nuclear shell theory has been very successful in explaining nuclear energy levels, nuclear decay, and the greater stability of nuclei with closed shells. We have been producing ever-heavier transuranic elements since the early 1940s, and we have now produced the element with Z = 118 size 12{Z="118"} {} . There are theoretical predictions of an island of relative stability for nuclei with such high Z size 12{Z} {} s.

Portrait of Maria Goeppert Mayer
The German-born American physicist Maria Goeppert Mayer (1906–1972) shared the 1963 Nobel Prize in physics with J. Jensen for the creation of the nuclear shell model. This successful nuclear model has nucleons filling shells analogous to electron shells in atoms. It was inspired by patterns observed in nuclear properties. (credit: Nobel Foundation via Wikimedia Commons)

Section summary

  • Two particles, both called nucleons, are found inside nuclei. The two types of nucleons are protons and neutrons; they are very similar, except that the proton is positively charged while the neutron is neutral. Some of their characteristics are given in [link] and compared with those of the electron. A mass unit convenient to atomic and nuclear processes is the unified atomic mass unit (u), defined to be
    1 u = 1.6605 × 10 27 kg = 931.46 MeV / c 2 .
  • A nuclide is a specific combination of protons and neutrons, denoted by
    Z A X N or simply A X, size 12{"" lSup { size 8{A} } X} {}
    Z size 12{Z} {} is the number of protons or atomic number, X is the symbol for the element, N size 12{N} {} is the number of neutrons, and A size 12{A} {} is the mass number or the total number of protons and neutrons,
    A = N + Z . size 12{A=N+Z} {}
  • Nuclides having the same Z size 12{Z} {} but different N size 12{N} {} are isotopes of the same element.
  • The radius of a nucleus, r size 12{r} {} , is approximately
    r = r 0 A 1 / 3 ,
    where r 0 = 1.2 fm . Nuclear volumes are proportional to A size 12{A} {} . There are two nuclear forces, the weak and the strong. Systematics in nuclear stability seen on the chart of the nuclides indicate that there are shell closures in nuclei for values of Z size 12{Z} {} and N size 12{N} {} equal to the magic numbers, which correspond to highly stable nuclei.

Conceptual questions

The weak and strong nuclear forces are basic to the structure of matter. Why we do not experience them directly?

Define and make clear distinctions between the terms neutron, nucleon, nucleus, nuclide, and neutrino.

What are isotopes? Why do different isotopes of the same element have similar chemistries?

Problems&Exercises

Verify that a 2 . 3 × 10 17 kg size 12{2 "." 3 times "10" rSup { size 8{"17"} } "kg"} {} mass of water at normal density would make a cube 60 km on a side, as claimed in [link] . (This mass at nuclear density would make a cube 1.0 m on a side.)

m = ρV = ρd 3 a = m ρ 1/3 = 2.3 × 10 17 kg 1000 kg/m 3 1 3 = 61 × 10 3 m = 61 km

Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter, taking this to be 2 . 3 × 10 17 kg/m 3 size 12{2 "." 3´"10" rSup { size 8{"17"} } " kg/m" rSup { size 8{3} } } {} .

What is the radius of an α size 12{α} {} particle?

1.9 fm size 12{1 "." 9" fm"} {}

Find the radius of a 238 Pu size 12{"" lSup { size 8{"238"} } "Pu"} {} nucleus. 238 Pu size 12{"" lSup { size 8{"238"} } "Pu"} {} is a manufactured nuclide that is used as a power source on some space probes.

(a) Calculate the radius of 58 Ni size 12{"" lSup { size 8{"58"} } "Ni"} {} , one of the most tightly bound stable nuclei.

(b) What is the ratio of the radius of 58 Ni size 12{"" lSup { size 8{"58"} } "Ni"} {} to that of 258 Ha size 12{"" lSup { size 8{"258"} } "Ha"} {} , one of the largest nuclei ever made? Note that the radius of the largest nucleus is still much smaller than the size of an atom.

(a) 4.6 fm size 12{4 "." "6 fm"} {}

(b) 0 . 61 to 1 size 12{0 "." "61 to 1"} {}

The unified atomic mass unit is defined to be 1 u = 1 . 6605 × 10 −27 kg size 12{1" u"=1 "." "6605"×"10" rSup { size 8{-"27"} } "kg"} {} . Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four-digit or better values for c size 12{c} {} and q e size 12{ lline q rSub { size 8{e} } rline } {} .

What is the ratio of the velocity of a β size 12{β} {} particle to that of an α size 12{α} {} particle, if they have the same nonrelativistic kinetic energy?

85 . 4 to 1 size 12{"85" "." "4 to 1"} {}

If a 1.50-cm-thick piece of lead can absorb 90.0% of the γ size 12{γ} {} rays from a radioactive source, how many centimeters of lead are needed to absorb all but 0.100% of the γ size 12{γ} {} rays?

The detail observable using a probe is limited by its wavelength. Calculate the energy of a γ size 12{γ} {} -ray photon that has a wavelength of 1 × 10 16 m size 12{1 times "10" rSup { size 8{ - "16"} } m} {} , small enough to detect details about one-tenth the size of a nucleon. Note that a photon having this energy is difficult to produce and interacts poorly with the nucleus, limiting the practicability of this probe.

12.4 GeV size 12{"12" "." "4 GeV"} {}

(a) Show that if you assume the average nucleus is spherical with a radius r = r 0 A 1 / 3 size 12{r=r rSub { size 8{0} } A rSup { size 8{1/3} } } {} , and with a mass of A size 12{A} {} u, then its density is independent of A size 12{A} {} .

(b) Calculate that density in u/fm 3 size 12{"u/fm" rSup { size 8{3} } } {} and kg/m 3 size 12{"kg/m" rSup { size 8{3} } } {} , and compare your results with those found in [link] for 56 Fe size 12{"" lSup { size 8{"56"} } "Fe"} {} .

What is the ratio of the velocity of a 5.00-MeV β size 12{β} {} ray to that of an α size 12{β} {} particle with the same kinetic energy? This should confirm that β size 12{β} {} s travel much faster than α size 12{β} {} s even when relativity is taken into consideration. (See also [link] .)

19.3 to 1

Questions & Answers

what is the meaning of function in economics
Effah Reply
Pls, I need more explanation on price Elasticity of Supply
Isaac Reply
Is the degree to the degree of responsiveness of a change in quantity supplied of goods to a change in price
Afran
Discuss the short-term and long-term balance positions of the firm in the monopoly market?
Rabindranath Reply
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Soumya
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Afran
what is firms
Anteyi Reply
A firm is a business entity which engages in the production of goods and aimed at making profit.
Avuwada
What is autarky in Economics.
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what is choice
Tia Reply
So how is the perfect competition different from others
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what is choice
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1
Naziru
what is the difference between short run and long run?
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It just depends on how far you would like to run!!!🤣🤣🤣
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Ada
Is this not economics?
Ukpen
This place is meant to be for serious educational matters n not playing ground so pls let's make it a serious place.
Docky
Is there an economics expert here?
Docky
Okay and I was being serous
Anna
The short run is a period of time in which the quantity of at least one inputs is fixed...
Anna
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Elacisity
salihu
Meaning of economics
Suraj Reply
It will creates rooms for an effective demands.
Chinedum Reply
different between production and supply
babsnof
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eshita
What is the economic?
Suraj
Economics is a science which study human behavior as a relationship between ends and scarce means which has an alternative use.
Mr
what is supply
babsnof
what is different between demand and supply
Debless Reply
Demand refers to the quantity of products that consumers are willing to purchase at various prices per time while Supply has to do with the quantity of products suppliers are willing to supply at various prices per time. find the difference in between
Saye
Please what are the effects of rationing Effect of black market Effects of hoarding
Atty Reply
monoply is amarket structure charecrized by asingle seller and produce a unique product in the market
Cali Reply
yes
Niraj
I want to know wen does the demand curve shift to the right
Nana
demand curve shifts to the right when there's an increase in price of a substitute or increase in income
kin
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kin
what are the factor that change the curve right
Nana
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freshwater
the Law of supply: states that all factor being equal, when the price of a particular goods increase the supply will also increase, as it decreases the supply will also decrease
kin
@Nana the factor that changes or shift the d demand curve to the right is 1) the increase in price of a substitute good or commodity 2) increase in income
kin
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kin
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define an apportunity cost?
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Cali
In a simple term, it is an Alternative foregone.
Sule
opportunity cost is the next best value of a scale of preference
Akiti
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Nelly
opportunity cost: is a forgone alternative
kin
Monopoly is where is one producer produces a given product with no close substitute
James
what is income effect?
Qwecou Reply
if you borrow $5000 to buy a car at 12 percent compounded monthly to be repaid over the next 4 year what is monthly payment
Nitish Reply
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
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The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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