please answer questions 1,2,&4

1) Show that an incremental energy increase of will cause an exponential decrease in the Maxwell-Boltzmann distribution according to: f(+)=f()e// 2) Show that the most probable value for the energy of a particle in an ideal monatomic gas is 1/2kT. How does this compare to the average energy and what is the reason for the difference? 3) Consider an ideal gas of hydrogen atoms. At what temperature will the number of atoms in the first excited state equal 1% of the number of atoms in the ground state? 4) Consider a metal with a simple cubic structure with atomic spacing d, and one electron per atom contributing to the electron gas/sea of electrons. Show that the DeBroglie wavelength of an electron at the Fermi energy is just over 2d