A) 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.

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.

The 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^3

The "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.

) 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?

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.

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.

The 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.

An 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.