Radioactivity, Radiation and the Structure of the atom

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1 Radioactivity, Radiation and the Structure of the atom What do you know (or can we deduce) about radioactivity from what you have learned in the course so far?

2 How can we learn about whether radioactive decay has occurred?

3 Understanding the emissions Radiochemistry : Field started as separation of different radioactive species from ores and one species from another. Discovery of Polonium (Po) a new element; Separation of radium from pitchblende (75% U 3 O 8 ). Some of the uranium undergoes fission. One of the products of the fission is barium, which can be separated by precipitation. From the barium one can separate radium. All of this early work in the field involved (radio)chemical separation techniques. Hence this area is called radiochemistry. Types of radiation: Based on the ability of the radiation to ionize air (as measured by an electroscope/electrometer) J.J. Thomson and others; Absorbtion by metal foils placed between the radioactive source and the electroscope. Alpha rays (α) : stopped by a few thousandths of Al foil. Beta rays (β): required 100 times more Al to be absorbed. Gamma rays (γ): even more penetrating Names provided by Rutherford

4 Deflection in electric and magnetic fields led to the realization that α and β rays were in fact streams of high speed particles and allowed determination of the charge and charge to mass ratio. Particle Charge Mass (rest) Comment β e= chg. On electron x10-28 g Same as electron α -2e Same as He 2+ Same as He +2 γ 0 0 Lorentz Force: F = q ( E + V B ) arrows indicate vector quantities What do these quantities mean?

5 J.J. Thomson, "Cathode Rays," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Fifth Series, October p. 296 Schematic drawing of Thomson's apparatus in the second experiment. Rays from the cathode (C) pass through a slit in the anode (A) and through a slit in a grounded metal plug (B). An electrical voltage is established between aluminum plates (D and E), and a scale pasted on the outside of the end of the tube measures the deflection of the rays. Cathode rays (electrons) could be bent by placing a voltage between the plates labeled D and E generating an electric field. V = where V is the voltage and is the distance between the plates E d Alternatively, the electrons can be deflected by a magnetic field. Key to making the experiments work was evacuating the gas in the tube as much as possible.

6 Discovery of neutron (existence predicted by Rutherford in 1920) By J. Chadwick, F.R.S. Proc. Roy. Soc., A, 136, p (Received May 10, 1932) [ Original papers: /Chadwick-neutron.html ] Bombarded a sample of beryllium with a source of alpha particles. The result was a penetrating radiation they called beryllium rays that required 200 mm of lead to be stopped. In contrast, a proton required only 1 mm of lead to be stopped. Chadwick showed that the beryllium rays were in fact uncharged particles and could not be gamma rays. For example, Be + 4 He C + n ; n = neutron

7 Coulomb s Law, Rutherford scattering, and the model of the atom Coulomb s Law : q1q2 V ( r) = r The potential energy, V, between two charges is proportional to the product of their charges (q 1 and q 2 respectively) and inversely proportional to the distance between them (r). Notice that opposite charges repel and opposite charges attract.. Notice the similarity and difference between Coulomb s Law and the equation for gravitational potential V ( r) = G m m 1 r 2 Force is the negative of the derivative of the potential with respect to position (r). F = dv dr Therefore the Coulomb interaction between two charges q1 and q2 is: q1q2 F ( r) = ; notice that a positive force is repulsive and a 2 r negative force is attractive!

Pt Reflector RaC source ZnS screen Microscope See also:

8 Thomson model of the atom Geiger and Marsden (Phil. Mag. 25, 605 (1913)) scattered α particles of different foils. Pt Reflector RaC source ZnS screen Microscope See also: /GeigerMarsden-1913.html

About 1 in 8000 incident alphas was scattered to a large angle and observed on the

Conclusion: The experiments indicated that the nucleus is a densely charged object,

Zαe 1 MαV 2 1 4 sin ( 0 2 2 φ α ) 2 n(φ) = number of alpha particles falling on a unit

n 0 = number of incident alpha particles t = thickness of the scatterer N = number of

9 About 1 in 8000 incident alphas was scattered to a large angle and observed on the screen. Conclusion: The experiments indicated that the nucleus is a densely charged object, otherwise these large deflections would not be possible. n( φ) = n Nt 16r Ze. Zαe 1 MαV sin ( φ α ) 2 n(φ) = number of alpha particles falling on a unit area at a distance r from the scattering point to the scattering angle φ. n 0 = number of incident alpha particles t = thickness of the scatterer N = number of nuclei per unit volume scatterer M α = mass of the alpha particle V α = initial velocity of the alpha particle Z α e = charge of the alpha particle Ze = charge of the scatterer What s happening physically?

10 First Law of Radioactivity and Concept of half-life dn dt = λn from observation; λ is a constant known as the decay constant. N( t) = N 0 e λt t ln(2) λ 1 / 2 = = λ Half-lives are a characteristic of a particular decay. For example, 40 K undergoes βdecay with a half-life of 1.27 x 10 9 years to transform itself into 40 Ca

12 NOTATION Nuclide is any combination of neutrons and protons A Z X N Atomic ionization state = Z-# of electrons Definitions -- Isotopes: Z is constant (e.g. 12 C, 13 C, 14 C) Isotones: N is constant (e.g. 11 B, 12 C, 13 N) Isobars: A is constant (e.g. 14 C, 14 N) NOTE: The mass of a nucleus is NOT its mass number!

13 What is the following device? What applications is it used in? What physical relation that we studied in the course is it associated with?

14 Chart of Nuclides: Not all combinations of neutrons and protons are allowed. Atomic Number Neutron Number Why do some combinations of neutrons and protons occur and not others?

Binding energy E=mc 2 ; mass and energy are equivalent c= velocity of light = 2.99792 x 10 10 cm/s 1 amu = 1.660 x 10-24 g E=(1.

15 Binding energy E=mc 2 ; mass and energy are equivalent c= velocity of light = x cm/s 1 amu = x g E=(1.660 x g)( x cm/s) 2 = x 10-3 erg 1 ev = x erg 1 amu = MeV Alternatively one may say that c 2 = MeV/u

16 Description Mass in g Mass in MeV Symbol m p Mass of proton x g m n Mass of neutron x g m e Mass of electron 9.1x10-28 g Note that there is a factor of ~ between the mass of an electron and a proton/neutron. Why is the mass of a proton less than the mass of a neutron?

17 Using mass tables Define: Mass Defect = Δ ; This is sometimes called the Mass Excess. = ( M A) c 2 units of Δ in MeV Or M = A + 2 c Units of M in amu abbreviated u Example: M( 4 He) = u, what is Δ? Δ = (M-A)c 2 = ( )u( MeV/u) = MeV Likewise, if you know Δ you can calculate M.

18 Taken From Nuclear Wallet cards, 5th ed J.K. Tuli (posted on class Website)

19 Chemical Atomic Weight M Z = i f i M i f i = relative abundance M i = mass of each isotope Example: f( 63 Cu) = % ; f( 65 Cu) = % ; M( 63 Cu) = ; M( 65 Cu) = Problem: Calculate <M Cu >.

20 Relativistic Effects Relativity says that if we increase the velocity of a particle, its total mass increases. This prediction is verified at accelerators. For example, for a 200 MeV proton at IUCF v=0.6c ; M/M 0 = 1.25 IN THIS COURSE WE WILL IGNORE RELATIVITY (except in a few special cases). use classical equations of motion: E = 1 2 M 0 V p = M 0V 2 expression for the kinetic energy of a particle with rest mass M 0 and velocity V expression for the momentum of a particle with rest mass M 0 and velocity V These approximations are not bad as long as v/c 0.1

21 Nuclear Binding Energies (What drives stability) 1. General Definition : Mass is converted into potential energy which holds the system together. Consequence for relative motions of particles in nucleus (Note that nucleons in nucleus are in constant motion.) Examples M(nucleus) < (ZMp + NMn) M(atom) < (M(nucleus) + ZMe) M(molecule) < Σ M (atoms) The difference in mass is what we call the BINDING ENERGY. (E=mc 2 )

22 2. Total Binding Energy: TBE TBE is the mass converted into energy when a nucleus is formed from its constituent nucleons and electrons. A Z X TBE 2 c Z 1 H + N 1 n + ; mass balance; LHS in u TBE ( A ZM + NM M ( X )) c 2 = ; energy balance; LHS in MeV H n Z Substituting M= A + Δ/c 2, TBE A = Z + N ( X ) ; analogous to the heat of condensation H n Z Reversing the equation defines nuclear vaporization TBE for the deuteron is 2.2 MeV TBE for 238 U is ~ 2000 MeV

Radioactivity, Radiation and the Structure of the atom

Radioactivity, Radiation and the Structure of the atom What do you know (or can we deduce) about radioactivity from what you have learned in the course so far? How can we learn about whether radioactive