Question

A bright star 20 light-years away emits violet light with wavelength of 380 nm as seen from the earth. A spaceship is covered with tinanium on its surface, whose work function is 4.3 eV.

a) When the spaceship is stationed on earth, determine whether photoelectrons are ejected from the spaceship due to the violet starlight. If so, compute their maximum kinetic energy.

b) The spaceship has just departed earth (with negligible travel distance so far) and is flying towards the star at a speed of 0.8 c. Calculate the maximum kinetic energy of the photoelectrons ejected from the spaceship as measured by the pilot of the spaceship.

c) If the pilot performs an experiment with these photoelectrons during a spacewalk near her spaceship, what is the probability for the most energetic photoelectrons to penetrate a 10 eV energy barrier that is 1 nm thick?

d) One of the most energetic photoelectrons is shooting precisely towards the star. In the reference frame of this electron, how long does it take (for the electron itself) to reach the star?

e) When this electron is arriving on the star, an alien there performs the same experiment as in part (c), using his 10 eV energy barrier that is 1 nm thick, what is the probability for the electron to penetrate that barrier?

1eV = 1.6×10−19 J

h = 6.626×10^−34 J· s = 4.135×10^−15 eV·s

h ̄ = 1.05×10^−34 J·s = 6.6×10^−16 eV·s

hc = 1240 nm · eV

me = 0.511 MeV – mass of the electron

KT = 1/40 eV at room temperature

E1 = −13.6 eV – ground state of the Hydrogen atom
a0 = 0.053 nm – radius of the Hydrogen atom in its ground state

Answer 1