CLRS 321 Nuclear Medicine Physics and Instrumentation 1 Unit I: Physics of Nuclear Medicine Lecture 2 Mass Energy Equivalence and Units CLRS 321 Nuclear Medicine Physics and Instrumentation 1

Lecture Objectives State the relationship of mass and energy in Einstein’s equation Relate mass defect to nuclear binding energy Recognize prefixes relating to different base-10 exponents and convert equivalent values between each Identify the units of measurement used in nuclear medicine physics Convert between conventional English and SI Units, particularly in regard to radioactivity and exposure

Mass Energy Equivalence (The Binding Energy of the Nucleus) The positively charged protons and the neutral neutrons have specific binding energies that hold them together in the nucleus. Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 14. A Helium atom is composed of two protons and two neutrons, plus a couple of electrons. Yet, the mass of two protons and two neutrons by themselves is more than the Helium nucleus (without the electrons). This is referred to as the mass defect. What’s behind it? Some of the mass of the protons and neutrons is being converted into energy, according to Einstein’s famous equation: E = mc2 This converted energy is the binding energy of the nucleus.

e⋅lec⋅tron-volt   –noun Physics. a unit of energy, equal to the energy acquired by an electron accelerating through a potential difference of one volt and equivalent to 1.602 × 10−19 joules. Abbreviation: eV, ev, Also, electron volt. Origin: 1925–30 Dictionary.com Unabridged Based on the Random House Dictionary, © Random House, Inc. 2009. In the radiological sciences, we usually measure energy in kilo (i.e. 1000) electron Volts, or keV; as well as Mega electron Volts (i.e. 1,000,000), or MeV. electronvolt. (n.d.). Dictionary.com Unabridged (v 1.1). Retrieved August 22, 2009, from Dictionary.com website: http://dictionary.reference.com/browse/electronvolt

Converting the Mass of an Electron to Energy (from your textbook) Rest mass of electron = 9.1 X 10-31kg (Energy) (Mass) (Speed of Light Squared)

Converting Electron Mass Continued We wanted our end unit in eV, but the unit we ended up with can is equivalent to a joule (joules can be converted to eV) Therefore:

Converting Electron Mass Continued Now we can convert joules to eV: We apply this to our electron energy: 5.112198 X 105 eV

Converting Electron Mass Continued Often atomic-mass level energy is expressed in Mega electron Volts (MeV), which is equivalent to a million electron Volts. So We can convert our eV to MeV with the following: Now we apply… 5.112198 X 105 5.112198 X 105 5.112198 X 5.112198 0.5112198

Converting Proton Mass to Energy (MeV) We won’t go through all the steps, but basically: Therefore, the energy equivalent of a proton’s mass is about 938 MeV

Converting Neutron Mass to Energy (MeV) Therefore, the energy equivalent of a neutron’s mass is about 941 MeV

Mass Defect of the Carbon Nucleus (example) AMUs were defined using the weight of a Carbon nucleus: 6 protons and 6 neutrons (12 nucleons) A carbon atom nucleus =12.00000 AMU A proton = 1.00759 AMUs A neutron = 1.00898 AMUs Therefore, 0.09942 AMU is unaccounted for based on Carbon’s standard of 12 AMU (Kahn Academy example: https://www.khanacademy.org/science/chemistry/nuclear-chemistry/radioactive-decay/v/mass-defect-and-binding-energy )

Mass Defect of the Carbon Nucleus (example) This extra mass (0.09942 AMU) is converted to binding energy which is holding the nucleus together. This difference is called the mass defect AMUs are simply another unit of mass, and we can convert it to kg based on: We will find the binding energy in class using E = mc2 1 AMU ≡ 1.66054 X 10-27 kg

Common Exponent Values in Nuclear Medicine Abbreviation Prefix Name Value Common term value Common Example p pico- 10-12 one trillionth pA (picoAmps) n nano- 10-9 one-billionth nm (nanometers) µ micro- 10-6 one millionth µCi (microCuries) m milli- 10-3 one thousanth mCi (milliCuries) c centi- 10-2 one hundreth cm (centimeters) k kilo- 103 a thousand keV (kilo electron Volts) M Mega- 106 a million MBq (Megabequerels) G Giga- 109 a billion GBq (Gigabequerels) T Tera 1012 a trillion TB (Terabyte)

Common Units in Nuclear Medicine Measured Item Common Old Unit SI Unit Conversion Factor Radioactivity milliCurie (mCi) Megabequerels (Mbq) 1 mCi ≡ 37Mbq Radiation Exposure (air kerma) Roentgen (R) Coulomb/kg 1 R ≡ 2.58 X 10-4 C/kg Radiation Absorbed Dose rad Gray (Gy) 1 rad ≡ 0.01 Gy Radiation Dose Equivalent rem Sievert (Sv) 1 rem ≡ 0.01 Sv Distance inch (in) Centimeter (cm) 1 in ≡ 2.54 cm Weight (mass) pound (lb) Kilogram (kg) 2.2 lb ≡ 1 kg

Homework 1 will be due in class, Monday, September 11th! Next Time…. Modes of Radioactive Decay. Homework 1 will be due in class, Monday, September 11th!