medical imaging dr. hugh blanton entc 4390. radiation and the atom

MEDICAL IMAGING

Dr. Hugh Blanton

ENTC 4390

Radiation and the Atom

Dr. Blanton - ENTC 4390 - RADIATION 3

What is Radiation?


Ionizing & Non-Ionizing Radiation

• Ionizing Radiation: Radiation is energy transmitted as particles or waves. Ionizing radiation has sufficient energy to dislodge orbital electrons, thereby producing ions. Examples: alpha, beta, gamma, neutron, and x-rays

Non-Ionizing Radiation: Radiation that does not have sufficient energy to dislodge orbital electrons. Examples: visible light, infra-red , micro-waves, radio-waves,

and radar

Dr. Blanton - ENTC 4390 - RADIATION 5 Page 19


Ionizing Radiation Hits An Atom

Incoming

Photon

EjectedElectro

n


Particles and Photons• Radiation can be in the form of particles or

waves (photons).

• The most common types of ionizing radiation are alpha, beta, gamma, neutron, and x-rays.

• Gamma and x-ray radiation are photons. They are part of the electromagnetic spectrum and considered packets of pure energy.

• Alpha, beta, and neutron radiation are particles having mass. Betas are electrons and alphas are helium nuclei.


Alpha Particles: 2 neutrons and 2 protons:

They travel short distances, have large massOnly a hazard when inhaled

Alpha Particles


Beta ParticlesBeta Particles: Electrons or positrons having small mass and variable energy. Electrons form when a neutron transforms into a proton and an electron:


Gamma RaysGamma Rays (or photons): Result when the nucleus releases Energy, usually after an alpha, beta or positron transition

A gamma particle is a photon. It is produced as a step in a radioactive decay chain when a massive nucleus produced by fission relaxes from the excited state in which it first formed towards its lowest energy or ground-state configuration.


X-RaysX-Rays: Occur whenever an inner shell orbital electron is removed and rearrangement of the atomic electrons results with the release of the elements characteristic X-Ray energy


***Electron-Volts (eV)*** When talking about subatomic particles, and individual photons,energies are very small (~10-12 or smaller).

It’s cumbersome to always deal with these powers of 10.

We introduce a new unit of energy, called the electron-volt (eV).

An [eV] is equivalent to the amount of energy a single electron gainswhen it is accelerated across a voltage of 1 [V].

Your TV tube accelerates electrons using 20,000 [V] = 20 [kV].

0 [kV]

-20 [kV]

10[J]

0 [J]

1 kgGPE

1 m0 [V]

-20 [kV]

+

-

ElectricPotential


More on [eV]How much energy does an electron gain when it is accelerated across a voltage of 20,000 [V] ?

E = 20,000 [eV][V] is a unit of “Potential”[eV] is a unit of Energy (can be converted to [J])

How can you convert [eV] to [J] ?Not too hard… the conversion is: 1 [eV] = 1.6x10-19 [J]


More on [eV]So, let’s do an example ! Convert 20 [keV] to [J]. Since the “k” == kilo = 1000 = 103, 20 [keV] = 20,000 [eV] = 2x104 [eV]

It’s a lot easier to say “20 [keV]” than 3.2x10-15 [J] !

-194 151.6x10 [J]2x10 [eV] 3.2 10 [J]

1 [eV]x

=1


Even more on [eV]So, [eV] IS A UNIT OF ENERGY;

It’s not a “type” of energy (such as light, mass, heat, etc).

When talking about energies of single photons, or of subatomic particles, we often use this unit of energy, or some variant of it.

So,

1 [eV] = 1.6x10-19 [J] (can be used to go back & forth between these two energy units)

1 [keV] = 1000 [eV] = 103 [eV] “k = kilo (103)””

1 [MeV] = 1,000,000 [eV] = 106 [eV] “M = mega (106)”

1 [GeV] = 1,000,000,000 [eV] = 109 [eV] “G = giga (109)”


Example 1A Cobalt-60 nucleus is unstable, and undergoes a decay where a 1173 [keV] photon is emitted. From what region of the electromagnetic spectrum does this come?


The energy is 1173 [keV], which is 1173 [keV] = 1173x103 [eV] = 1.173x106

[eV].

* First convert this energy to [J],

E = 1.173x106 [eV] * (1.6x10-19 [J] / 1 [eV]) = 1.88x10-13 [J]

* Now, to get the wavelength, we use: E = hc/, that is = hc/E.

So, = 6.63x10-34[J s]*3x108[m/s]/1.88x10-13 [J] = 1.1 x 10-12 [m]

* Now, convert [m] to [nm], 1.1 x 10-12 [m] * (109 [nm] / 1 [m]) = 1.1x10-3 [nm]

It’s a GAMMA Ray


Example 2An electron has a mass of 9.1x10-31 [kg].

E = mc2 = 9.1x10-31*(3x108)2 = 8.2x10-14 [J] Now convert to [eV]

-14 5

-19

1 [eV]8.2x10 [J] 5.1x10 [eV]=0.51 [MeV]1.6x10 [J]

What is an electron’s rest mass?

m = E / c2 = 0.51 [MeV/c2]

According to Einstein, m = E/c2, that is:[mass] = [Energy] / c2

What is it’s rest mass energy in [J] and in [eV].


Example 3A proton has a mass of 1.67x10-27 [kg].

E = mc2 = 1.67x10-27 *(3x108)2 = 1.5x10-10 [J] Now convert to [eV]

-10 8

-19

1 [eV]1.5x10 [J] 9.4x10 [eV]=940 [MeV]1.6x10 [J]

What is a proton’s rest mass?

m = E / c2 = 940 [MeV/c2]

According to Einstein, m = E/c2, that is:[mass] = [Energy] / c2

What is it’s rest mass energy in [J] and in [eV].


Proton vs Electron MassHow much more massive is a proton than an electron ?

Ratio = proton mass / electron mass

= 940 (MeV/c2) / 0.51 (MeV/c2) = 1843 times more massive

You’d get exactly the same answer if you used:

electron mass = 9.1x10-31 [kg]

Proton mass = 1.67x10-27 [kg]

Using [MeV/c2] as units of energy is easier…


Neils Bohr and the Quantum Atom

1885-1962

Pointed out serious problems with Rutherford’s atom Electrons should radiate as they orbit the nucleus, and in doing so, lose energy, until they spiral into the nucleus.Atoms only emit quantized amounts of energy (i.e., as observed in Hydrogen spectra)

He postulated Electric force keeps electrons in orbit Only certain orbits are stable, and they do not radiate energy

Radiation is emitted when an e - jumps froman outer orbit to an inner orbit and the energydifference is given off as a radiation.

Awarded the Nobel Prize in 1922

Circa 1910-1925


Electrons circle the nucleus due to the Electric force

Bohr’s Picture of the Atom

Allowed Orbits

12

34

5n =

Electronin lowest“allowed”

energy level(n=1)

Electronin excited

state(n=5)

Before

12

34

5

Electron falls to the lowest

energy level

AfterRadiatedphoton

Note: There are many more energy levels beyond n=5, they are omitted for simplicity


Atomic RadiationIt is now “known” that when an electron is in an “excited state”,it spontaneously decays to a lower-energy stable state.

Beforen = 1

n = 2

n = 3

n = 4

n = 5

Energy Electronin excited

state(higher

PE)

E5

E4

E2

E3

E1

E5 > E4 > E3 > E2 > E1

Aftern = 1

n = 2

n = 3

n = 4

n = 5

Energy Electronin lowest

state(lower PE)

E5

E4

E2

E3

E1

One example could be:


The difference in energy, E, is given by:

E = E5 – E1 = hphoton

h = Planck’s constant = 6.6x10-34 [J s] = frequency of light [hz]

The energy of the light is DIRECTLY PROPORTIONAL to the frequency, .

Recall that the frequency, , is related tothe wavelength by:

c = c

So, higher frequency higher energy lower wavelength

This is why UV radiation browns your skinbut visible light does not !


Hydrogen atom energy “levels”Quantum physics provides the tools to compute the values ofE1, E2, E3, etc…The results are:

En = -13.6 / n2

Energy Level Energy En (eV)

1 -13.62 -3.43 -1.514 -0.855 -0.54

These results DO DEPEND ON THE TYPE OF ATOM OR MOLECULE

12

34

5


Hydrogen atom energy “levels”

So, the difference in energy between the 3rd and 1st quantum state is:

Ediff = E3 – E1 = -1.51 – (-13.6) = 12.09 (eV)

When this 3 1 atomic transition occurs, this energy is released in the form of electromagnetic energy.


Example 4

E = 12.1 [eV]. First convert this to [J].

-19181.6x10 [J]12.1 [eV] 1.94 10 [J]

1 [eV]x

Since E = h = E/h, so:

= E/h = 1.94x10-18 [J] / 6.6x10-34 [J s] = 2.9x1015 [1/s] = 2.9x1015 [hz]

In the preceding example, what is the frequency, wavelength of theemitted photon, and in what part of the EM spectrum is it in?


Example 4

= c/= (3x108 [m/s]) / (2.9x1015 [1/s]) = 1.02x10-7 [m] = 102 [nm]

This corresponds to low energy X-rays !

medical imaging dr. hugh blanton entc 4390. radiation and the atom

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