Chapter 30 Nuclear Physics AP Physics B Lecture Notes

Chapter 30Nuclear Physics

AP Physics B Lecture Notes

29-01 Some Properties of Nuclei

29-02 Binding Energy

29-03 Radioactivity

29-04 The Decay Process

Nuclear Physics

Sections

Chemical symbol

Atomic numberProtons

Atomic massprotons + neutrons

XAZ

The nucleus:

Number of neutrons = A - Z

The size of the nucleus

3

115 A m 10x 1.2r

Nuclear Physics 30

Some Properties of Nuclei

Nucleus is made of protons and neutrons

Neutron is electrically neutral: kg 10x 1.67493m 72P

The radius of the nucleus

3

115 Am 10x 1.2r

kg 10x 1.6605u 1 72Atomic mass unit

2c

MeV 5.319

kg 10x 1.67262m 72P

Proton has positive charge:

Nuclear Physics 30


Chapter 29: Nuclear Physics

An atom's atomic number is determined by the number of

(A) neutrons in its nucleus.

(B) nucleons in its nucleus.

(C) protons in its nucleus.

(D) alpha particles in its nucleus.

From the following table, you can see that the electron is considerably less massive than a nucleon.

Nuclear Physics 30



If an atom's atomic number is given by Z, its atomic mass by A, and its neutron number by N, which of the following is correct?

(A) N = A - Z

(B) N = Z - A

(C) N = A + Z

(D) none of the given answers

The total mass of a stable nucleus is always less than the sum of the masses of its separate protons and neutrons.

PPN

N

An Alpha particle

P P NN

u 007825.12H m2 11 u 017330.12m2 n

u 015650.2 u 017330.2

u 032980.4u 002603.4mα

Nuclear Physics 30

Binding Energy

This difference between the total mass of the constituents and the mass of the nucleus is called the total binding energy of the nucleus.

u 002603.4mα u 032980.4mparts

u 030377.0mΔ

Binding energy

2cmΔE

Energy released

uMeV

931.5 u 030377.0 MeV 28.30

Nuclear Physics 30

Binding Energy

To compare how tightly bound different nuclei are, we divide the binding energy by A to get the binding energy per nucleon.

Nuclear Physics 30

Binding Energy

The higher the binding energy per nucleon, the more stable the nucleus.

More massive nuclei require extra neutrons to overcome the Coulomb repulsion of the protons in order to be stable.

The force that binds the nucleons together is called the strong nuclear force. It is a very strong, but short-range, force. It is essentially zero if the nucleons are more than about 10-15 m apart.

Nuclear Physics 30

Binding Energy

Calculate the binding energy per nucleon for a nucleus of

N147

Binding Energy

b) Calculate the total binding energy, and the binding energy per nucleon, for Pb208

82

Binding Energy


Compared to the masses of its separate protons and neutrons, the total mass of a stable nucleus is always

(A) less.

(B) the same.

(C) greater.

(D) zero.


When nucleons join to form a stable nucleus, energy is

(A) destroyed.

(B) absorbed.

(C) released.

(D) not transferred.

Nuclei that are unstable decay; many such decays are governed by another force called the weak nuclear force.

Radioactive rays were observed to be of three types:

Gamma radiation are electromagnetic radiation and can penetrate several centimeters of lead

Beta radiation are electrons and can penetrate 3 mm of aluminum

Alpha radiation are helium nuclei and can barely penetrate a piece of paper

Nuclear Physics 30

Radioactivity

Alpha and beta rays are bent in opposite directions in a magnetic field, while gamma rays are not bent at all.

Nuclear Physics 30

Radioactivity


Beta rays can penetrate

(A) air only.

(B) a piece of paper.

(C) several centimeters of lead.

(D) several millimeters of aluminum.


Gamma rays can penetrate

(A) air only.


(C) several millimeters of aluminum.

(D) several centimeters of lead.

Example of alpha decay:

Radium-226 will alpha-decay to radon-22

He Ra Ra 42

22286

22688

Nuclear Physics 30

The Decay Process

In general, alpha decay can be written:

Alpha decay occurs when the strong nuclear force cannot hold a large nucleus together. The mass of the parent nucleus is greater than the sum of the masses of the daughter nucleus and the alpha particle; this difference is called the disintegration energy.

He Y X 42

4A2Z

AZ

Alpha decay is so much more likely than other forms of nuclear disintegration because the alpha particle itself is quite stable.

Nuclear Physics 30

The Decay Process

Beta decay occurs when a nucleus emits an electron. An example is the decay of carbon-14:

The nucleus still has 14 nucleons, but it has one more proton and one fewer neutron.

ν e Ra C 01-

147

146

In general, beta decay can be written:

ν e Y X 01

A1Z

AZ

ν e p n 01-

11

10

The fundamental process is a neutron decaying to a proton, electron, and neutrino:

Nuclear Physics 30

The Decay Process

Beta decay can also occur where the nucleus emits a positron rather than an electron:

ν e F eN 01

199

1910

The fundamental process is a proton decaying to a neutron, positron, and neutrino:

ν e n p 01

10

11

The nucleus still has 19 nucleons, but it has one more neutron and one fewer protons.

In general, positron emission can be written:

ν e Y X 01

A1Z

AZ

Nuclear Physics 30

The Decay Process

And a nucleus can capture one of its inner electrons:

ν iL e eB 73

01

74

The fundamental process in an electron capture:

ν n e p 10

01

11

The nucleus still has 7 nucleons, but it has one more neutron and one fewer protons.

In general, positron emission can be written:

ν Y e X A1Z

01

AZ

Nuclear Physics 30

The Decay Process

Gamma rays are very high-energy photons. They are emitted when a nucleus decays from an excited state to a lower state, just as photons are emitted by electrons returning to a lower state.

γ N N 126

126

In general, gamma emission can be written:

γ X X AZ

AZ

Nuclear Physics 30

The Decay Process

What is the maximum KE of the emitted b particle during the decay of Co60

27

The Decay Process

How much recoil energy does a nucleus get when it emits a 1.46 MeV gamma ray?

K4019

The Decay Process

The number of decays in a short time interval is proportional to the number of nuclei present and to the time:

Here, l is a constant characteristic of that particular nuclide, called the decay constant.

Half-Life and Rate of DecayNuclear decay is a random process; the decay of any nucleus is not influenced by the decay of any other.

tΔNλNΔ

Nuclear Physics 30

The Decay Process

This equation can be solved, using calculus, for N as a function of time:

Half-Life and Rate of Decay

tλoeNN

The half-life is the time it takes for half the nuclei in a given sample to decay. It is related to the decay constant:

λ2ln

T21

λ693.0

Nuclear Physics 30

The Decay Process

Carbon-14 has a half-life of 5730 years. What is the activity of a sample that contains 3.1 x 1020 nuclei?

The Decay Process

What fraction of a sample is left after exactly 6 half-lives?

The Decay Process

Phosphorus-32 has a half-life of 1.23 x 106 s. Calculate the activity of a pure 9.7 mg sample.

The Decay Process


Gamma rays can penetrate

(A) air only.


(C) several millimeters of aluminum.

(D) several centimeters of lead.


During β- decay

(A) a neutron is transformed to a proton.

(B) a proton is transformed to a neutron.

(C) a neutron is ejected from the nucleus.

(D) a proton is ejected from the nucleus.


When a β+ particle is emitted from an unstable nucleus, the atomic number of the nucleus

(A) increases by 1.

(B) decreases by 1.

(C) does not change.

(D) none of the given answers

Nuclei contain protons and neutrons – nucleons

Total number of nucleons, A, is atomic mass number

Number of protons, Z, is atomic number

Nuclear masses are measured in u; carbon-12 is defined as having a mass of 12 u

An alpha particle is a helium nucleus; a beta particle is an electron or positron; a gamma ray is a highly energetic photon

Unstable nuclei decay through alpha, beta, or gamma emission

Difference between mass of nucleus and mass of its constituents is binding energy

Nuclear Physics 30

Summary

Nuclei are held together by the strong nuclear force; the weak nuclear force is responsible for beta decay

Electric charge, linear and angular momentum, mass-energy, and nucleon number are all conserved

Radioactive decay is a statistical process

The number of decays per unit time is proportional to the number of nuclei present:

tλoeNN Nλ

tΔNΔ

The half-life is the time it takes for half the nuclei to decay

Nuclear Physics 30

Summary

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Chapter 30 Nuclear Physics AP Physics B Lecture Notes