Physics 1C End of Chapter 30 Exam Preparationds
Radioactive Decay Example The isotope 137 Cs is a standard laboratory source of gamma rays. The half-life of 137 Cs is 30 years. (a) How many 137 Cs atoms are in a 5.0μCurie source? (b) What is the activity of the source 10 years later?! Answer! Recall that the number of atoms for 137 Cs will decay exponentially.
! Answer Radioactive Decay! Start by getting everything in the proper SI units:! Next, turn to the half-life formula to find the decay constant:
! Answer Radioactive Decay! Finally, turn to the activity equation to solve for the number of atoms remaining:
! Answer Radioactive Decay! Now for part (b) we should again convert everything in SI units:! We should then look at how the activity will decrease over time:
Decay and Nuclear Reactions! When one element changes into another element, the process is known as a spontaneous decay.! Nuclear reactions occur when you combine elements to form different elements.! For both decays and nuclear reactions, the mass number, A, must be the same on both sides of the equation.! Also, the sum of the atomic numbers, Z, must be the same on both sides of the equation.! Basically, charge, momentum, and mass-energy must be conserved in both processes.
Alpha Decay! In alpha decay, for example, the nucleus emits an alpha particle (He nucleus).! By the conservation laws, the nucleus will lose two protons and two neutrons. (N decreases by 2, Z decreases by 2, and A decreases by 4).! Symbolically, this becomes: A X A 4 Y+ Z Z 2 4 2 He! Where, X is called the parent nucleus and Y is called the daughter nucleus.! Momentum needs to be conserved as well.
Beta and Gamma Decay! In beta decay the nucleus emits a beta particle (electron or positron).! Thus, there will be the same number of nucleons in the daughter nucleus as the parent nucleus, but the atomic number is changed by one.! Symbolically: A Z A Z X X A Z+ 1 A Z 1! In gamma decay the nucleus emits a gamma particle (photon). Gamma emission doesn t change the A or Z of a nucleus. Y Y + + e e +
Nuclear Reactions! In nuclear reactions both A and charge are conserved:! The energy required to balance a nuclear reaction is called the Q-value of the reaction. Q = ( Δm)c 2 = ( m m )c 2 initial final! In an exothermic reaction, energy is released which leads to mass loss. This will yield a positive Q-value.! In an endothermic reaction, energy is absorbed, which leads to mass gain. This will yield a negative Q-value.
Concept Question! A sample starts with 1,000 radioactive atoms. How many half-lives have elapsed when 750 atoms have decayed?! A) 0.25! B) 1.5! C) 2.0! D) 2.5! E) 3.0
Exam Preparation The most useful way to prepare is to go through: All the suggested homework problems All the practice problems for quizzes All the even problems in the book, i.e. those that have answers in the back. I will add additional practice problems to the web site during the weekend, and a practice final on Monday evening.
Exam Rules You write your own equations sheet. This can maximally be 2 pages. Bring a Scantron, your ID, and write your proper quiz code number on your form.
Exam Review
Things We Have Learned! 1) Simple Harmonic Motion:! For a mass on a spring, the force on the mass will be given by:! In general, anything that exhibited simple harmonic motion:! F = F! restoring = ( constant) ( displacement)! The periods of SHM can be: T spring = 2π m k T pend = 2π L g
Things We Have Learned! 2) Waves:! We represent a traveling wave with a sine wave.! We relate wavelength, wave speed, and frequency by: v wave = λ T = λf
Things We Have Learned! 3) Sound:! Sound waves are longitudinal waves traveling through a medium.! Sound waves interfere. The resulting wave is the sum of the amplitudes of the two initial waves.! When the source or the observer is moving, the frequency will change: " v f o = f sound ± v o s $ # v sound v s % ' &! Standing waves occur under wave reflection such that nodes and anti-nodes are created:
Things We Have Learned! 4) Reflection and Refraction:! When light is reflected off of a surface it will be reflected at an angle given by: θ 1 = # θ 1! When light moves between two different media, the light will be refracted at an angle given by: n 1 sinθ 1 = n 2 sinθ 2! Remember that all angles are measured with respect to the normal!
Things We Have Learned! 5) Mirrors and Lenses:! Mirrors use the reflection of light to divert the light rays. 1 p + 1 q = 1 f M = h " h = q p! Lenses use the refraction of light to divert the light rays.! Ray diagrams may be useful:! Sign conventions are important
Things We Have Learned! 6) Wave Interference:! The wave nature of light leads to interference effects.! These can be caused by a path length difference or a phase shift.! Double slit interference was due to a path length difference. δ = mλ = dsinθ! Thin film interference was due to both: Con. for 1 phase change Des. for 1 phase change 2nt = ( m + 1 2)λ For m = 0, 1, 2...
Things We Have Learned! 8) Quantum Physics:! Light exhibits wave-particle duality.! Experiments such as the photoelectric effect and the Compton effect demonstrate the particle nature of light.! Experiments like double-slit interference and Bragg s X-ray scattering demonstrate the wave nature of light.! Light energy is quantized into discrete units known as photons.! Matter of a given momentum also has wave properties. E n = nhf λ = h p = h mv
Things We Have Learned! 9) Atomic Physics:! Emission spectral lines were always at particular wavelengths for certain elements. 1 λ = R H & 1 $ % nf 2 1 n 2 i #! "! Bohr took this information and decided the atom must be quantized. r n = n 2! 2 E m e k e e 2 tot = 1 # 2 k e 2 & 13.6 ev % e ( = $ n 2 a o ' n 2! The states an electron is allowed to occupy in an atom are described by the principal quantum number, n, but also includes other quantum numbers (l, m l, ms).
Things We Have Learned! 10) Nuclear Physics:! Rutherford s thin-foil experiment demonstrated that the nucleus is small and dense.! Stable nuclei can be categorized by the amount of binding energy per nucleon they have. Q = ( Δm)c 2 = ( m m )c 2 initial final! There are three types of radioactivity: alpha, beta, and gamma.! They decay via: N = N o e λt
Concept Question! In a single-slit diffraction experiment, as the width of the slit is made smaller, the width of the central maximum of the diffraction pattern:! A) becomes smaller.! B) becomes wider.! C) remains the same.! D) There will be no diffraction pattern on the screen since the apparatus and screen distance are set up for a particular width.