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Phet explorations: nuclear fission

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Nuclear Fission

Section summary

  • The binding energy (BE) of a nucleus is the energy needed to separate it into individual protons and neutrons. In terms of atomic masses,
    BE = { [ Zm ( 1 H ) + Nm n ] m ( A X ) } c 2 ,
    where m 1 H size 12{m left ("" lSup { size 8{1} } H right )} {} is the mass of a hydrogen atom, m A X is the atomic mass of the nuclide, and m n is the mass of a neutron. Patterns in the binding energy per nucleon, BE / A , reveal details of the nuclear force. The larger the BE / A size 12{"BE"/A} {} , the more stable the nucleus.

Conceptual questions

Why is the number of neutrons greater than the number of protons in stable nuclei having A greater than about 40, and why is this effect more pronounced for the heaviest nuclei?

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Test prep for ap courses

Binding energy is a measure of how much work must be done against nuclear forces in order to disassemble a nucleus into its constituent parts. For example, the amount of energy in order to disassemble H 2 4 e MathType@MTEF@5@5@+=feaagyart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0raaSqaaiaaikdaaeaacaaI0aaaaOGaaeisaiaabwgaaaa@3958@ into 2 protons and 2 neutrons requires 28.3 MeV of work to be done on the nuclear particles. Describe the force that makes it so difficult to pull a nucleus apart. Would it be accurate to say that the electric force plays a role in the forces within a nucleus? Explain why or why not.

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Problems&Exercises

2 H is a loosely bound isotope of hydrogen. Called deuterium or heavy hydrogen, it is stable but relatively rare—it is 0.015% of natural hydrogen. Note that deuterium has Z = N size 12{Z=N} {} , which should tend to make it more tightly bound, but both are odd numbers. Calculate BE/ A , the binding energy per nucleon, for 2 H and compare it with the approximate value obtained from the graph in [link] .

1.112 MeV, consistent with graph

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56 Fe is among the most tightly bound of all nuclides. It is more than 90% of natural iron. Note that 56 Fe has even numbers of both protons and neutrons. Calculate BE/ A , the binding energy per nucleon, for 56 Fe and compare it with the approximate value obtained from the graph in [link] .

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209 Bi is the heaviest stable nuclide, and its BE / A is low compared with medium-mass nuclides. Calculate BE/ A , the binding energy per nucleon, for 209 Bi and compare it with the approximate value obtained from the graph in [link] .

7.848 MeV, consistent with graph

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(a) Calculate BE / A for 235 U , the rarer of the two most common uranium isotopes. (b) Calculate BE / A for 238 U . (Most of uranium is 238 U .) Note that 238 U has even numbers of both protons and neutrons. Is the BE / A of 238 U significantly different from that of 235 U ?

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(a) Calculate BE / A for 12 C . Stable and relatively tightly bound, this nuclide is most of natural carbon. (b) Calculate BE / A for 14 C . Is the difference in BE / A between 12 C and 14 C significant? One is stable and common, and the other is unstable and rare.

(a) 7.680 MeV, consistent with graph

(b) 7.520 MeV, consistent with graph. Not significantly different from value for 12 C , but sufficiently lower to allow decay into another nuclide that is more tightly bound.

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The fact that BE / A is greatest for A near 60 implies that the range of the nuclear force is about the diameter of such nuclides. (a) Calculate the diameter of an A = 60 nucleus. (b) Compare BE / A for 58 Ni and 90 Sr . The first is one of the most tightly bound nuclides, while the second is larger and less tightly bound.

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The purpose of this problem is to show in three ways that the binding energy of the electron in a hydrogen atom is negligible compared with the masses of the proton and electron. (a) Calculate the mass equivalent in u of the 13.6-eV binding energy of an electron in a hydrogen atom, and compare this with the mass of the hydrogen atom obtained from [link] . (b) Subtract the mass of the proton given in [link] from the mass of the hydrogen atom given in [link] . You will find the difference is equal to the electron’s mass to three digits, implying the binding energy is small in comparison. (c) Take the ratio of the binding energy of the electron (13.6 eV) to the energy equivalent of the electron’s mass (0.511 MeV). (d) Discuss how your answers confirm the stated purpose of this problem.

(a) 1 . 46 × 10 8 u vs. 1.007825 u for 1 H

(b) 0.000549 u

(c) 2 . 66 × 10 5 size 12{2 "." "66" times "10" rSup { size 8{ - 5} } } {}

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Unreasonable Results

A particle physicist discovers a neutral particle with a mass of 2.02733 u that he assumes is two neutrons bound together. (a) Find the binding energy. (b) What is unreasonable about this result? (c) What assumptions are unreasonable or inconsistent?

(a) –9.315 MeV

(b) The negative binding energy implies an unbound system.

(c) This assumption that it is two bound neutrons is incorrect.

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Questions & Answers

Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
Alexia Reply
how would I work this problem
Alexia
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
Igor
what is angular velocity
Obaapa Reply
Why does earth exert only a tiny downward pull?
Mya Reply
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Islam
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
Kintu
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
Obrian Reply
what is power?
aron Reply
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
Alona Reply
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
Kavita Reply
hi
Godfred
what about the wind vane
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
Anurag Reply
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
Jaydie Reply
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
Princewill Reply
Practice Key Terms 2

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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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