Chapter 15, Problem 25P

1. For centuries, we accpeted Newton's 2nd Law as the standard model for motion. Then Einstien came along and siggested a modification in cases of high velocity. The Lorenz factor:                                         γ(v)=(1/square-root of 1−(v^2/c^2)) a) The constant (c) is the speed of light, which is 3 * 10^8 m/s. What is the lim as v approaches 400 γ(v)? You will have to track many decimal places to see a difference from 1. A bullet travels 400 m/s; this limit indicates that time dilation is extremely small (and basically negigible) at that speed.    b) In the movie Interstellar, time dialation occurs as 1 hour on the water planet corresponds to 7 years on earth. What is the factor γ in this case (what is the ratio of 7 years to 1 hour)?   c) If we rearrange the equation for γ and solve for v, we get:                                    v = c square-root of (γ^2 - 1/γ^2) What velocity v is necesary to get the γ you found in part (b)?   d) What is the lim as v approaches c γ(v) ?…

A galaxy G is moving away radially with speed with respect to an observer O. The relation between X, the wavelength of light emitted at G, and λo, the wavelength observed at O, is 入。 λ = λe λε 1+B 1- B' = where ẞ v/c (c is the speed of light). For ẞ < 1 find a power series expansion of the above formula up to and including terms of order ẞ³.

The Sun's mass is1.989 ×10^8 and it radiates at a rate of 3.827×10^23 kW. a) From this data, assuming it converts all its mass into energy,  what is the estimate the lifetime of the Sun? b) Theoretical calculations predict the Sun's lifetime (in its current stage) to be about 5 billion years. During that time, what percentage of its mass will it lose?

A star’s spectrum emits more radiation with a wavelength of 690.0 nm than with any other wavelength.   If the star is 9.78 ly from Earth and its radius is 7.20 × 108 m, what will an Earth-based observer measure for this star’s intensity? Stars are nearly perfect blackbodies. (Note: ly stands for light-years.) Answer in W/m2

An alpha particle is the nucleus of a He-4 atom and has a rest mass of 3727.38 MeV/c2. How much energy is required to accelerate an alpha particle from rest to 0.6c? What is the momentum of the alpha particle once it reaches this speed? Would more, less or the same amount of energy be required to accelerate a proton from rest to this speed?

Note: m=93 4. A particle of charge q = moves in velocity i = (2+ m)î - (5 + m)j – 4k in magnetic field B = (7+ m)j + 2k and electric field Ē = 5î – j + (2 + m)k. a. Compute the Lorentz force experienced by the particle b. The magnitude of this force

A muon is a short-lived particle. Muons are created by cosmic rays; they can also be created by particle accelerators. The muon is similar to an electron but has a larger mass: mμ ≈ 200me. During its brief lifetime, a muon can combine with a proton to create a system that is similar to atomic hydrogen called a muonic hydrogen atom. The larger mass of the muon makes some of the assumptions of the Bohr hydrogen atom treatment less accurate, but using the mathematics of the Bohr hydrogen atom to analyze this system will give approximate results that allow us to understand how the changing mass affects the properties of the system. How does the energy required to ionize a muonic hydrogen atom compare to that required to ionize a regular hydrogen atom?A. It is greater.B. It is approximately the same.C. It is less.

A hydrogen atom undergoes a transition from an excited state to the ground state by emitting a photon. The energy difference between the excited state and the ground state is 2.04 eV. The wavelength of the emitted photon is measured to be 656 nm. Calculate the frequency and the energy of the emitted photon in Joules. (Note: You may use the following conversions: 1 eV = 1.6 x 10^-19 J and the speed of light, c = 3.0 x 10^8 m/s) Give your answer to the nearest whole number.

A muon is a short-lived particle. Muons are created by cosmic rays; they can also be created by particle accelerators. The muon is similar to an electron but has a larger mass: mμ ≈ 200me. During its brief lifetime, a muon can combine with a proton to create a system that is similar to atomic hydrogen called a muonic hydrogen atom. The larger mass of the muon makes some of the assumptions of the Bohr hydrogen atom treatment less accurate, but using the mathematics of the Bohr hydrogen atom to analyze this system will give approximate results that allow us to understand how the changing mass affects the properties of the system. The larger mass of the muon complicates an accurate mathematical treatment similar to that of the Bohr hydrogen atom becauseA. The de Broglie wavelength of the muon is shorter than that of the electron.B. The relatively small difference in mass between the muon and the proton means that we can’t ignore the motion of the proton.C. The short lifetime of the muon…