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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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what is inorganic
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Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
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can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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progressive wave
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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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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