Forces in a Nucleus - albert

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Fundamentals of Radiation

Partial Periodic Table

Alkali

Metals

1A

1

H

1.01

Hydrogen

Alkaline

Earth

Metals

IIA

3

Li

6.94

Lithium

4

Be

9.01

Beryllium

IIIA

5

B

10.81

Boron

6

C

12.01

Carbon

Atomic

Chemical

Atomic

Name of

Number

Symbol

Mass

Element

Noble Gases

0

IVA

6

C

12.01

Carbon

VA

7

N

14.01

Nitrogen

VIA

8

O

16.00

Oxygen

VIIA

9

F

19.00

Flourine

2

He

4.00

Helium

10

Ne

20.18

Neon

The Periodic Table provides the atomic number (Z), the chemical symbol, atomic mass, and element name. It also groups the elements based on their electron structure (I.e., how they react chemically).

Structure of the Atom

Nucleus

The nucleus contains neutrons and protons, also referred to as nucleons. The electrons orbit the nucleus.

The electrons are responsible for chemical reactions (e.g., formation of molecules).

The protons have a positive charge, the electrons a negative charge, and the neutrons are not charged.

Orbiting Electrons

The nucleons are responsible for nuclear reactions (e.g., radioactive decay).

Nomenclature

Z = Number of Protons

(determines the chemical element)

N = Number of Neutrons

(determines the isotope of the element)

A = Neutrons plus Protons

(atomic mass of the isotope)

A = Z + N

A

Z

X

N

X = Chemical Symbol

The chemical symbol and the atomic mass define the individual nuclide . (e.g., 3 H has 1 proton and 2 neutrons).

Isotopes of an element have the same number of protons, but a different number of neutrons in the nucleus.

Forces in a Nucleus

Nuclear force is an attractive force between each of the nucleons (i.e., neutrons and protons) over relatively short distances.

p

Nuclear force of neutron on proton n n Nuclear force of proton on neutron

Hydrogen-3 (Tritium)

Electrostatic force is a repulsive force between the like charged protons over a greater distance than nuclear forces.

Electrostatic force of proton on proton p

Nuclear force of proton on proton n p Nuclear force of proton on proton

Electrostatic force of proton on proton

Helium - 3

Radioactive Decay

The nuclides, as with most things in nature, want to be at their lowest energy state which is a stable nucleus.

Radioactive decay occurs in nuclides where the nucleus is unstable.

For stable nuclides with low atomic masses, the number of neutrons is equal to, or approximately equal to the number of protons (except for 1 H which only has one nucleon).

As the atomic mass of the nuclide increases, the ratio of neutrons to protons must be greater than one for it to be stable, suggesting that more neutrons are required to provide nuclear forces to offset the electrostatic repulsive force between the increased number of protons.

The nucleus may also become unstable when energy is added to it, placing it in an excited state. An example of this would be a free moving neutron inside of a reactor being captured by the nucleus of a 238 U nucleus.

The nuclide reaches its stable state by undergoing radioactive decay.

Types of Radiation

There are four types of radiation of interest:

1) Alpha (

) which is a positively charged helium nucleus (2 protons and 2 neutrons).

2) Beta (

) which is a negatively charged electron.

3) Gamma (

) which is a packet of energy with zero rest mass.

4) Neutron (n) which is a released neutron. Mainly a concern during nuclear reactor operation.

Alpha Particle

Helium-4 Nucleus

 (2 neutrons, 2 protons)

Slow moving, but high energy

Cannot penetrate material easily

 Stopped by one piece of paper

 Stopped by dead layer of skin

Example of Alpha Decay

Radium-226

(88 protons, 138 neutrons)

Alpha particle

Radon-222

(86 protons, 136 neutrons)

Alpha decay occurs when the nuclides of high atomic mass have a lower neutron to proton ratio than stable nuclides and ejects an alpha particle.

Alpha decay is rare for nuclides with low or intermediate mass numbers.

Beta Particle

Electron

Fast moving, Medium energy

Can penetrate material well

 Stopped by 100 to 150 pieces of paper

 Stopped by 0.5 -1 centimeter of water

Example of Beta Decay

Carbon - 14

(6 protons, 8 neutrons)

Beta particle

Nitrogen - 14

(7 protons, 7 neutrons)

Beta decay occurs when the nuclides have a higher neutron to proton ratio than stable nuclides.

A neutron converts to a proton, electron (

), and a neutrino.

A neutrino is a high energy particle with zero rest mass with high penetrating capability.

Gamma Decay

Electromagnetic radiation

 Similar to light, x-rays, radio waves

Emitted only by certain nuclei

Speed of light; low to high energy

Highly penetrating

 Stop half of the

 s with about 1 cm of lead

 or 5 to 15 cm of water

Example of Gamma Decay

238 U + neutron

239 U +

Gamma decay occurs as a means of removing energy from the nucleus of an excited nuclide.

The gamma may be ejected alone or in conjunction with the emission of another radioactive particle (e.g.,

) to reduce the nucleus energy.

Examples of Neutron

Emission

There are Neutron (n) emissions associated with the following reactions.

2 H +

 

1 H + neutron

9 Be +

 

2 ( 4 He) + neutron

9 Be +

 

12 C + neutron

Neutron emissions of interest in a nuclear reactor occur when the excited nucleus of a specific high atomic mass nuclide splits into two or more smaller nuclides during the fission process.

235 U + n

135 I + 97 Y + 3n

Neutrons with high kinetic energy are released in the process.

Half-life

Each radioactive nucleus has a certain probability of decay per time

Some decay quickly (fractions of a second), some later (thousands of years)

Rate of decay depends on the number of nuclei available

As number decreases, rate of decay decreases

Half-life

In theory, all the radioactive material will never totally decay

Define Half-life

 Time for half of the sample to decay

Half-life

1

1

16

1

8

1

4

1

2

1 2 3

Time (Number of half-lives)

4

Example Half-lives -

Natural

Uranium-238 (In soil)

 4.5 Billion years

Potassium-40 (in soil and body)

 1.3 Billion years

Carbon-14 (In all living tissue)

 5730 years

Hydrogen-3 (in all water)

 12 years

Example Half-lives -

Natural

Radium-226 (In soil - produces radon)

 1600 years

Radon-222 (in soil and air)

 3.8 days

Polonium-214 (radon progeny that decays in lungs)

 164 microseconds (0.000164 s)

Example Half-lives -

Medical Uses

Iodine - 131 (Thyroid treatment)

 8 days

Technetium-99m (Nuclear medicine)

 6 hours

Gold-198 (Tumor therapy)

 2.7 days

Activity

Activity = Decays per time

Units:

 1 Becquerel = 1 decay per second (dps)

 1 Curie = 37 Billion dps

 1 microCurie ( m

Ci) = 37,000 dps

 1 picoCurie (pCi) = 0.037 dps

Example Activities -

Regulations

Typical maximum alpha emitting radionuclide allowed without a license

(some exceptions)

 0.1 m

Ci

Typical maximum beta emitting radionuclide allowed without a license

(some exceptions)

 10 m

Ci

Example Activities - Natural

Radioactivity

Uranium-238 in cup of soil (typical)

 0.003 m

Ci = 3000 pCi

Radon-222 in air

 0.5 pCi per liter (outdoor air)

 1 to hundreds of pCi per liter (houses)

Potassium-40 in human body

 0.1 m

Ci

Radiation Dose

Dose = Energy absorbed per mass

Units:

 Rad

 Gray (Gy) [1 Gy = 100 rad)

Radiation Dose Equivalent

Different radiations do different amounts of biological damage

Dose Equivalent = Dose X QF

QF = Quality factor

 Betas, Gamma: QF = 1; Alpha: QF = 20

Units

 Rem (1 mrem = 0.001 rem)

 Sievert (Sv) [1 Sv = 100 rem)]

Radiation Exposure

Old unit of exposure

 Amount of radiation present in air

 Only applicable for x-rays and gamma radiation

Units:

 Roentgen (R)

 1 R exposure in air will produce about 1 rad dose in human tissue

Example Doses

Natural annual background radiation

 cosmic: 27 mrem (0.27 mSv)

 Terrestrial: 28 mrem (0.28 mSv)

 Internal: 39 mrem (.039 mSv)

 [total natural (excl. Radon): ~100 mrem]

 Radon-lungs: 2400 mrem (24 mSv)

[effective whole body: 200 mrem]

 Source: NCRP Report #93

Example Doses

Medical Radiation (Effective Whole

Body Dose Equivalent)

 Chest X-ray: 8 mrem (0.08 mSv)

 Head CT scan: 111 mrem (1.11 mSv)

 Barium Enema: 406 mrem (4.06 mSv)

 Extremity X-ray: 1 mrem (0.01 mSv)

 Source: NCRP Report 100

Radiation Safety

Radioactive materials produce a dose rate per time

To reduce total dose:

 Minimum time

 Half the time - half the dose

 Shielding

 Maximum distance

 Twice the distance - one-fourth the dose

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