I am not too sure if these questions correspond to each other, so i posted them

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I am not too sure if these questions correspond to each other, so i posted them all and the answers i got correct. i am looking for the answer to #4 which i will post below.


#2. An electron has a speed of 0.53 c. (The rest energy for an electron is 0.511 MeV, and the rest energy of a proton is 938.3 MeV.)
(a) Find the speed of a proton that has the same kinetic energy as the electron. (answer = 0.014141 c)
(b) Find the speed of a proton that has the same momentum as the electron. (answer = 104 km/s)

#3. In the ground state of hydrogen, the uncertainty in the position of the electron is roughly 0.10 nm. If the speed of the electron is approximately the same as the uncertainty in its speed, about how fast is it moving? (answer = 10^6 m/s)

#4.
Find the speed of an electron having a de Broglie wavelength equal to its Compton wavelength. (Hint: This electron is relativistic.)

Explanation / Answer

db = h / p

c = h / mc

Equating both

p = mc

mv = mc

Hence, Velocity of electron is approximately equal to the speed of light (c)

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