Calculations of protons

Question

A proton is accelerated through a voltage of 248 kV.

a) Calculate the energy of the proton in electron volt and in Joule.

b) Assuming that the mass of the proton remains the same as its rest mass, calculate the speed of the photon.

c)The proton is curved by a magnetic field of 1.5 Telsa. Calculate the radius of the curvature of its path.

Answer 1

(a)

K = eV

e = 1.6 x 10^-19 C

V = 248,000 volts

Plug in the numbers in the given units and get K in joules, then convert joules to electron volts recalling that

1 electron volt = 1.6 x 10^-19 joules

(b)

I assume you meant to ask for the the speed of the PROTON, not the PHOTON.

mv²/2 = K ⇒

v = √(2K/m)

Plug in the result for K from part (a). Look up in your physics book the rest mass of a proton in appropriate units and plug that in for m.

(c)

The magnetic force must equal the centripetal force, so

evB = mv²/r ⇒

r = mv/(eB)

Plug in the numbers in appropriate units. If you use B in Teslas, you want m in kg, v in m/s, and e in coulombs.