Formula Sheet 2 PDF

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Formula Sheet...

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Formula Sheet Constants: will be provided on the exam sheet. Transformer: ΔV2 = (N2/N1)ΔV1 Where ΔV1 & N1 are the voltage and number of turns in the primary and ΔV2 and N2 are the voltage and number of turns in the secondary Power: P= IΔV (in an ideal transformer, the power in the primary is equal to the power in the secondary. Electromagnetic Spectrum: Wavelength (λ): From shortest to longest wavelength: gamma, x-ray, ultraviolet, visible, infrared, microwave, radio Frequency: f = c/λ where c is the speed of light Energy: E = hf where h is Planck’s constant Doppler Effect: fo = fs(1 ± u/c) where fo is the observed frequency, fs is the source frequency, and u is the relative speed between the source and observer. Law of Reflection: θi = θr where θi is the angle of incidence and θr is the angle of reflection Index of Refraction: n = c/v where c is the speed of light in a vacuum and v is the speed of the light in a medium. Snell’s Law: n1 sinθ1 = n2 sinθ2 Total Internal Reflection: sinθc = n2/n1 where θc is the critical angle. Mirrors: 𝟏 𝒇

𝟏

𝟏

= + 𝒒 where f is the focal length, p is the object distance, and q is the image distance 𝒑

Mirror Sign Convention:

Magnification: !! ! (h’ is the image height and h is the object height) M=-!= !

Lenses: Equations are the same as mirrors. Lens Sign Convention

Young’s Double Slit: d is the distance between the slits and m is the order number of the fringe d sinθ = mλ (Constructive Interference) d sinθ = (m + ½) λ (Destructive Interference) Thin Film Interference: 2n t = (m + ½ ) λ m = 0, 1, 2 … Constructive interference with one phase change 2 n t = m λ m = 0, 1, 2 … Destructive Interference with one phase change where n is the index of refraction and t is the thickness of the film Single Slit Diffraction: The angles θ at which the diffraction pattern has zero intensity are: ! sin θdark = m where a is the slit width !

Special Relativity: Time Dilation: Δt = γ Δtp where Δt is the dilated time and Δtp is the proper time ! γ= ! !

!! ! !

Length Contraction: L = Lp/γ Momentum: p = γ mv Rest Mass: ER = mc2 Total Mass: E = γ mc2 Kinetic Energy is the difference between the total energy and the rest energy. Wien’s Law: λmax T = 0.2898 x 10-2 m K Photoelectric Effect: KEmax = hf - φ

where T is temperature in kelvin

where φ is the work function of the metal, h is Planck’s constant

deBroglie Wavelength: (matter wavelength) ! where p is the momentum and h is Planck’s constant λ= !

Uncertainty Principle: Δx Δp ≥ h/4π or ΔE Δt ≥ h/4π Bohr Model of the Atom: !!".! !" for hydrogen Energy: En = ! !

!!".! !"

En = (Z2) for hydrogen-like atoms where Z is the number of protons !! Radius of Orbital: rn = ao n2 where ao = 0.0529 nm Quantum Numbers: Principle: 1 ≤ 𝑛 < ∞ Orbital: 0 ≤ 𝑙 ≤ 𝑛 − 1 Magnetic: −𝑙 ≤ 𝑚! ≤ 𝑙 Nuclear Physics: Radius of the nucleus: 𝑟 = 𝑟! 𝐴!/! where 𝑟! = 1.2 𝑥 10!!" 𝑚 𝑎𝑛𝑑 𝐴 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑡𝑜𝑚𝑖𝑐 𝑛𝑢𝑚𝑏𝑒𝑟 Radioactive Decay Rate: 𝑁 = 𝑁! 𝑒 !!" where 𝑁 the # of radioactive nuclei present at time 𝑡, 𝑁! is the # at 𝑡 = 0 and 𝜆 is the decay constant for a given substance !.!"! Half-life: 𝑇!/! = !

Decay Processes: α decay = stream of Helium nuclei, β minus = stream of electrons, β plus = stream of positrons (anti-electrons). Total number of nucleons must be conserved as well as total charge. Energy: 𝑬 = 𝒎𝒄𝟐 : energy comes from a mass difference...