The relativistic mass is almost identical to the rest mass.
If the rest mass is exactly 6.64000 x 10⁻²⁷ kg, then the relativistic
mass, rounded to the third significant figure, is 6.65 x 10⁻²⁷ kg.
a). Kinetic energy = (1/2) (mass) (speed)²
Speed = (0.046) x (299,792,458 m/s)
KE = (1/2) (6.65 x 10⁻²⁷) (1.902 x 10¹⁴) = 6.32 x 10⁻¹³ joule
b). (6.32 x 10⁻¹³ joule) x (6.242 x 10¹⁸ eV/joule) = 3.947 x 10⁶ eV
c). 1 elementary charge = 1.60 x 10⁻¹⁹ Coulomb
Charge of 1 Helium nucleus = 2 elementary charges = 3.20 x 10⁻¹⁹ C.
6.32 x 10⁻¹³ joule / 3.20 x 10⁻¹⁹ C = 1,975,000 joule/Coulomb
= 1,975 kV .
That's an awful lotta volts for a straight accelerator.
I see two possibilities:
a). I made a mistake in my orders of magnitude. If so, I leave it
to you to find my mistake. I feel that I've already contributed enough
to earn 5 points.
b). If the math is true, then in order to accelerate alpha particles to
3.95 MeV, you'll need some sort of a pulsed scheme, as in a cyclotron,
synchrotron, or the LHC if you can buy some time.
You're not too generous with your points, are you Pap3, or whatever
your name is today, bless your shiny roboticles.
