<< 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, 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 math number
Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Concepts of physics with linear momentum. OpenStax CNX. Aug 11, 2016 Download for free at http://legacy.cnx.org/content/col11960/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Concepts of physics with linear momentum' conversation and receive update notifications?

Ask