The Modern Quantum Atom The nucleus and the discovery of the neutron What are electron-volts ? The Quantum atom

***Electron-Volts (eV)***  When talking about subatomic particles, and individual photons, energies are very small (~ 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 gains when it is accelerated across a voltage of 1 [V].  Your TV tube accelerates electrons using 20,000 [V] = 20 [kV]. 0 [kV] -20 [kV] 0 [V] -20 [kV] + - Electric Potential

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] = 1.6x [J] So, let’s do an example ! Convert 20 [keV] to [J]. Since the “k” == kilo = 1000 = 10 3, 20 [keV] = 20,000 [eV] = 2x10 4 [eV] It’s a lot easier to say “20 [keV]” than 3.2x [J] ! =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] = 1.6x [J] (can be used to go back & forth between these two energy units) 1 [keV] = 1000 [eV] = 10 3 [eV] “k = kilo (10 3 )”” 1 [MeV] = 1,000,000 [eV] = 10 6 [eV] “M = mega (10 6 )” 1 [GeV] = 1,000,000,000 [eV] = 10 9 [eV] “G = giga (10 9 )”

Example 1 A 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] = 1173x10 3 [eV] = 1.173x10 6 [eV]. * First convert this energy to [J], E = 1.173x10 6 [eV] * (1.6x [J] / 1 [eV]) = 1.88x [J] * Now, to get the wavelength, we use: E = hc/, that is = hc/E. So, = 6.63x [J s]*3x10 8 [m/s]/1.88x [J] = 1.1 x [m] * Now, convert [m] to [nm], 1.1 x [m] * (10 9 [nm] / 1 [m]) = 1.1x10 -3 [nm]  It’s a GAMMA Ray

Example 2 An electron has a mass of 9.1x [kg]. E = mc 2 = 9.1x *(3x10 8 ) 2 = 8.2x [J] Now convert to [eV] What is an electron’s rest mass? m = E / c 2 = 0.51 [MeV/c 2 ] According to Einstein, m = E/c 2, that is: [mass] = [Energy] / c 2 What is it’s rest mass energy in [J] and in [eV].

Example 3 A proton has a mass of 1.67x [kg]. E = mc 2 = 1.67x *(3x10 8 ) 2 = 1.5x [J] Now convert to [eV] What is a proton’s rest mass? m = E / c 2 = 940 [MeV/c 2 ] According to Einstein, m = E/c 2, that is: [mass] = [Energy] / c 2 What is it’s rest mass energy in [J] and in [eV].

Proton vs Electron Mass How much more massive is a proton than an electron ? Ratio = proton mass / electron mass = 940 (MeV/c 2 ) / 0.51 (MeV/c 2 ) = 1843 times more massive You’d get exactly the same answer if you used: electron mass = 9.1x [kg] Proton mass = 1.67x [kg] Using [MeV/c 2 ] as units of energy is easier…