Lecture 3 Date: 9/13/2024 Content: p = 1.673 x 10^-27 g, n = 1.675 x 10^-27 g, e- = 9.1 x 10^-31 g 1 amu = 1.6605 x 10^-24 g (12C-12) roughly, p+ mass C-12 + n = 12.00866 amu, 13.00866 amu C-13 ΔE = Δmc² Δm = 13.00866 - 12.009 = 0.91066 amu Binding energy affects mass 931.5 MeV = 1 amu (E=mc²) C-12 = 12.01 amu, weighted avg of isotopes Thermodynamic Stability: ΔE between reactants and products; ΔE does not correspond w/ rate of reaction. Kinetic Stability: involves energy barrier and reaction rate. Ex. in deuterium, a p+ and n are held together and have very-E nuclear binding energy (2.5 MeV) To be put in to pull nucleons apart, E needed E = m x c²; E = m x c²; magnitude large enough to detect in nuclear reactions. -2.5 MeV 1. Using the C-12 mass scale, an H-atom weighs 1.0078 amu. If an amu was defined as the mass of a H-atom, C-12's mass would be... less than 12.000 amu 2. For a nuclear reaction to be spontaneous, the products' mass must be... less than the reactants' mass Release in E to form C-12 lost mass, not as much in H Mass Spectrometry A diagram showing the process of mass spectrometry: a sample is ionized, accelerated, and then deflected in a magnetic field based on its mass-to-charge ratio. "Curvature depends on mass & charge (only +1)" "Larger mass → less bending" "# of each isotope → abundance" Isotopes of Neon (Ne) ²⁰Ne: 19.99244 amu ²¹Ne: 20.99395 amu ²²Ne: 21.99132 amu Abundance: ²⁰Ne: 90.48%, ²¹Ne: 0.27%, ²²Ne: 9.25% Isotopes of Chlorine (Cl) ³⁵Cl: 34.9689 amu ³⁷Cl: 36.9659 amu Abundance: ³⁵Cl: 75.5%, ³⁷Cl: 24.5% Probability of finding two ³⁵Cl: 0.755 x 0.755 = 0.57 Probability of finding one ³⁵Cl and one ³⁷Cl: 2 x 0.755 x 0.245 = 0.37 Probability of finding two ³⁷Cl: 0.245 x 0.245 = 0.06 Mass Spectrum of C₄H₁₀ (Butane) A graph showing the relative abundance of different ions detected in the mass spectrum of butane. Peaks are labeled with their corresponding mass-to-charge ratios (m/z). 58: Parent ion (C₄H₁₀) 57: C₄H₉⁺ (loss of one H) 43: C₃H₇⁺ (loss of a methyl group) 29: C₂H₅⁺ (ethyl fragment) 15: CH₃⁺ (methyl fragment) "Cannot determine relative abundance of fragments to each other" To determine amount of parent ion & fragment ions, control velocity of colliding electrons. 1. Which of the following is a parent ion of Cl₂? 36 + 35 = 70 36 + 37 = 71 37 + 37 = 74 Kinetic Stability: How long (half-life) (t₁/₂) Thermodynamic Stability: Spontaneous (ΔE < 0), ΔE = Δm - c² A nucleus can be thermodynamically unstable but kinetically stable. Thermodynamically unstable w/ respect to forming p+ + e- n → p+ + e- 1.00865 amu → 1.00777 amu Is spontaneous (and unstable) both thermodynamically & kinetically. 2. ¹H → ²H → ⁴He → ⁹Be (Masses ≠ sum of subatomic parts) 2.0026 amu → 4.0026 amu → 8.0246 amu, not spontaneous, E = mc² 8.0062 amu → 8.0246 amu, ΔP is increased, ΔE = + Exception: Usually larger elements more stable Nuclear Binding Energy (NBE): E needed to ionize/remove an e- to break bonds. He = 2p+ + 2n NBE > for more nucleons (compare w/ NBE/nucleon) ¹H + ¹H → ²He + ΔE 2p+ + 2n + ΔE = 4.0030 0.03038 amu ΔE, Δm = + Electrostatics have no effect on mass ¹H stability ²H (-) more E to get to 0 adding → no effect