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A typical carbon nucleus contains 6 neutrons and 6 protons. The 6 protons are all positively charged and in very close proximity, with separations on the order of 10 -15 meters, which should result in an enormous repulsive force. What prevents the nucleus from dismantling itself due to the repulsion of the electric force?

  1. The attractive nature of the strong nuclear force overpowers the electric force.
  2. The weak nuclear force barely offsets the electric force.
  3. Magnetic forces generated by the orbiting electrons create a stable minimum in which the nuclear charged particles reside.
  4. The attractive electric force of the surrounding electrons is equal in all directions and cancels out, leaving no net electric force.

(a)

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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?

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

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

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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

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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} } } {} .

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

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

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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.

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(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"} {}

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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 } {} .

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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"} {}

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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?

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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"} {}

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(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"} {} .

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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

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(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?

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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