<< Chapter < Page Chapter >> Page >

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 ( W = Fd cos θ size 12{W= ital "Fd""cos"θ} {} ), 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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!


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
Got questions? Get instant answers now!

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} } } {} .

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

(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"} {}

Got questions? Get instant answers now!

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 } {} .

Got questions? Get instant answers now!

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"} {}

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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"} {}

Got questions? Get instant answers now!

(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"} {} .

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

(a) What is the kinetic energy in MeV of a β size 12{β} {} ray that is traveling at 0.998 c ? This gives some idea of how energetic a β size 12{β} {} ray must be to travel at nearly the same speed as a γ ray. (b) What is the velocity of the γ ray relative to the β size 12{β} {} ray?

Got questions? Get instant answers now!

Questions & Answers

how lesers can transmit information
mitul Reply
griffts bridge derivative
Ganesh Reply
below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
Timothy Reply
what is a conductor
below me
why below you
no....I said below me ...... nothing below .....ok?
dust particles contains both positive and negative charge particles
corona charge can verify
when pressure increases the temperature remain what?
Ibrahim Reply
what is frequency
Mbionyi Reply
define precision briefly
Sujitha Reply
CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.
hope this helps
what's critical angle
Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
dude.....next time Google it
okay whatever
pls who can give the definition of relative density?
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
What is momentum
aliyu Reply
mass ×velocity
it is the product of mass ×velocity of an object
how do I highlight a sentence]p? I select the sentence but get options like copy or web search but no highlight. tks. src
Sean Reply
then you can edit your work anyway you want
Wat is the relationship between Instataneous velocity
Oyinlusi Reply
Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
The potential in a region between x= 0 and x = 6.00 m lis V= a+ bx, where a = 10.0 V and b = -7.00 V/m. Determine (a) the potential atx=0, 3.00 m, and 6.00 m and (b) the magnitude and direction of the electric ficld at x =0, 3.00 m, and 6.00 m.
what is energy
Victor Reply
hi all?
energy is when you finally get up of your lazy azz and do some real work 😁
what is physics
faith Reply
what are the basic of physics
base itself is physics
tree physical properties of heat
Bello Reply
tree is a type of organism that grows very tall and have a wood trunk and branches with leaves... how is that related to heat? what did you smoke man?
algum profe sabe .. Progressivo ou Retrógrado e Acelerado ou Retardado   V= +23 m/s        V= +5 m/s        0__>              0__> __________________________>        T= 0               T=6s

Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?