As it's going way slower than light speed, we can ignore relativistic effects (e.g., no increase in inertia). So the total energy E = e + k = .511 + .5*.511*(1.02E5/299E6)^2 = ? MeV.
Then from E = hF = ch/L and L = hc/E = 1240/(.511 + .5*.511*(1.02E5/299E6)^2) = 2430 nm. ANS.
NOTE kinetic energy k = 1/2 mv^2 = 1/2 .511 (v/c)^2 where electron rest mass m = e/c^2 = .511 MeV/c^2. Note also that total energy E = e(1 + 1/2 (v/c)^2) where e = .511 MeV.
Answers & Comments
As it's going way slower than light speed, we can ignore relativistic effects (e.g., no increase in inertia). So the total energy E = e + k = .511 + .5*.511*(1.02E5/299E6)^2 = ? MeV.
Then from E = hF = ch/L and L = hc/E = 1240/(.511 + .5*.511*(1.02E5/299E6)^2) = 2430 nm. ANS.
NOTE kinetic energy k = 1/2 mv^2 = 1/2 .511 (v/c)^2 where electron rest mass m = e/c^2 = .511 MeV/c^2. Note also that total energy E = e(1 + 1/2 (v/c)^2) where e = .511 MeV.