Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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The Compton wavelength, λc, of a particle of mass m is defined as follows: λc = h/mc. (a) Calculate the Compton wavelength of a proton. (b) Calculate the energy of a photon that has the same wavelength as found in part (a). (c) Show, in general, that a photon with a wavelength equal to the Compton wavelength of a particle has an energy that is equal to the rest energy of the particle.
Find Relative error for the find planck constant: h = (1.60217662 x 10^-19)(4.1628 10^-6 ±1.25718 10^-7)/(299792458)
Calculate the wavelength of electrons accelerated through 1742 V. (electron mass m = 9.1 x 10-31 Kg, electronic charge e=1.6 x 10-19 C and the Planck constant h=6.6 x 10-34 Js)
Round off the answer to 2 decimal places and write answers as power of 10.
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- In the LHC, protons are accelerated to a total energy of 7.80 TeV. The mass of proton is 1.673 × 10−27 kg and Planck’s constant is 6.626 × 10−34 J·s. In the reference frame of the protons, how long does it take the protons to go around the tunnel once? I know the answer is 10.8ns. The solutions posted on here, do not come within 1% of that answer so I cannot trust that the steps are correct. Please give step by step instructions on how to arrive at 10.8 nsarrow_forwardThe photons that make up the cosmic microwave background were emitted about 380,000 years after the Big Bang. Today, 13.8 billion years after the Big Bang, the wavelengths of these photons have been stretched by a factor of about 1100 since they were emitted because lengths in the expanding universe have increased by that same factor of about 1100. Consider a cubical region of empty space in today's universe 1.00 m on a side, with a volume of 1.00 m³. What was the length so of each side and the volume V of this same cubical region 380,000 years after the Big Bang? So = Vo = Enter numeric value Today the average density of ordinary matter in the universe is about 2.4 × 10-27 kg/m³. What was the average density po of ordinary matter at the time that the photons in the cosmic microwave background radiation were emitted? Po = m m³ kg/m³arrow_forwardA) What is the approximate wavelength emitted from helium represented by the bright yellow emission line below? What is it's frequency in HZ and energy in eV? (1 eV= 1.6 x 10-19 joules). B) If the excited helium electron that emits a yellow photon in this line starts with a potential energy of 8 eV, what is the potential energy of the electron afterwards? Assume that the emission of a yellow photon is allowed by the laws of quantum mechanics. Also don't worry about the other electron.arrow_forward
- A photon in a laboratory experiment has an energy of 4.2 eV. What is the frequency of this photon? Planck’s constant is 6.63 × 10−34 J · s. Answer in units of Hz.arrow_forwardThe photons that make up the cosmic microwave background were emitted about 380,000 years after the Big Bang. Today, 13.8billion years after the Big Bang, the wavelengths of these photons have been stretched by a factor of about 1100 since they were emitted because lengths in the expanding universe have increased by that same factor of about 1100. Consider a cubical region of empty space in today’s universe 1.00 m on a side, with a volume of 1.00 m3. What was the length s0 of each side and the volume V0 of this same cubical region 380,000 years after the Big Bang? s0 = ? m V0 = ? m^3 Today the average density of ordinary matter in the universe is about 2.4×10−27 kg/m3. What was the average density ?(rho)0 of ordinary matter at the time that the photons in the cosmic microwave background radiation were emitted? (rho)0 = ? kg/m^3arrow_forwardThe "classical" radius of a neutron is about 0.81 fm (1 femtometer = 10-15 m). The mass of a neutron is 1.675×10-27 kg. a) Assuming the neutron is spherical, calculate its density in kilograms per cubic meter. b) What would be the magnitude of the acceleration due to gravity, in meters per second squared, at the surface of a sphere of radius R = 1.2 m with this same density? Recall that the gravitational constant is G = 6.67 × 10-11 m3/kg/s2.arrow_forward
- A particle has γ=2,865. a) Calculate c-v in m/s. If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 2,910 MeV/c, calculate its energy in MeV.arrow_forward) a) What temperature is required for a black body spectrum to peak in the X-ray band? (Assume that E = 1 keV). What is the frequency and wavelength of a 1 keV photon? b) What is one example of an astrophysical phenomenon that emits black body radiation that peaks near 1 keV? c) What temperature is required for a black body spectrum to peak in the gamma-ray band with E = 1 GeV? What is the frequency and wavelength of a 1 GeV photon? d) What is one example of an astrophysical phenomenon that emits black body radiation that peaks at 1 GeV?arrow_forwardThe energy density distribution function in terms of frequency for blackbody radiation is described by the formula Planck derived, given as: p(v,T) = c3 exp(hu/kT)-1 Specify what each of the parameters or variables (i.e. {h, c, k, v,T}) are called in this equation. You may have to look this up, since we did not cover this in the lectures or book. What is the dimension of h? Sketch what this distribution function looks like as a function of v. You can do this with information given.arrow_forward
- A blackbody (a hollow sphere whose inside is black) emits radiation when it is heated. The emittance (Mλ, W/m3), which is the power per unit area per wavelength, at a given temperature (T, K) and wavelength (λ, m) is given by the Planck distribution, where h is Planck's constant, c is the speed of light, and k is Boltzmann's constant. Determine the temperature in degrees Celsius at which a blackbody will emit light of wavelength 3.57 μm with an Mλ of 5.31×1010 W/m3. The power per unit area emitted can be determined by integrating Mλ between two wavelengths, λ1 and λ2. However, for narrow wavelength ranges (Δλ), the power emitted can be simply calculated as the product of Mλ and Δλ. power emitted=MλΔλ Using the conditions from the first part of the question, determine the power emitted per square meter (W/m2) between the wavelengths 3.56 μm and 3.58 μm.arrow_forwardAsaparrow_forwardAn FM radio station broadcasts at 84 megahertz (MHz). What is the energy of each photon in Joule? Use h = 6.6 × 10-34 J·s for the Planck constant.arrow_forward
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