- 1 -Midterm #11. [4 points] The muon has a lifetime of 2 2106.×−s in its rest frame, after which it decaysinto an electron and two neutrinos.(a) How far does it travel at a velocity vc=098. before decaying? The velocity anddistance are measured in a laboratory considered to be at rest.(b) Calculate the kinetic energy available in the muon decay in the rest frame of themuon (not the laboratory frame). The muon has a mass 207 times larger than theelectron (m cµ2106= MeV ). The neutrinos are considered massless.Name:_______________________PHY3101me= ×−911 1031. kge= ×−160221019. Ch= ×−662611034. J-sme=0511. MeV / c2W = q Vh= ×−413571015. eV-smµ=106 MeV / c21 eV J= ×−160221019.hc=1240 eV-nmc= ×30108.m/s 1 MeV = 106 eVh= = ×−h / .2 10546 1034π J - sλν = c 1 GeV = 109 eVh= ×−65821 1016. eV-s1 nm = 109−m REhc∞= = ×07109737 10. m-1ame00221040 53 10= = ×−πε h. m1 MHz = 106s-1λT= ×−2898 103. m- Kγ =−1122vcdx xxxsin sin22142z= −Some useful constants and relations:- 2 -2. [4 points] The work function for magnesium is φ = 3.7 eV.(a) What is the threshold frequency for the photoelectric effect on magnesium?(b) What is the stopping potential if the wavelength of the incident light is 248 nm?3. [3 points] Estimate the surface temperature of the Sun if the emitted electromagneticradiation peaks at a wavelength of 500 nm.4. [3 points] Calculate the wavelength of the first spectral line in Balmer series, which is atransition from n = 3 to n = 2 in the Bohr model.- 3 -5. [3 points] Electromagnetic radiation of wavelength 102.5 nm is incident upon thehydrogen atom in its ground state. What is the highest state to which hydrogen can beexcited?6. [3 points] Calculate the deBroglie wavelength of a muon travelling at a velocity ofvc=098.. The muon has a mass 207 times larger than the electron (m cµ2106= MeV ).7. [3 points] An unstable particle called the Z particle is measured to have an average massof 91 GeV with a spread of 2.5 GeV (energy width) around this value. What is theminimum bound on its lifetime? (1 GeV = 109 eV).8. [3 points] An electron is located to a precision of 0.5×10-10 m along the x-axis. What isthe minimum uncertainty of its velocity along this axis?- 4 -9. [4 points] The wavefunction of a particle contained in a one-dimensional box of length Lis ψ π( ) sin( / )x A x L=3 . Sketch this function from x=0 to x=L. Sketch the intensity ofthis wavefunction (probability density). Determine the constant A if the particle existsonly in this