Question

The mass of a proton is 1.67 x 10^-27 kg
a.) find the energy equivalent in joules
b.) convert the answer from a.) into eV

Answer 1

a) This question uses Einstein's famous mass-energy duality equation, E=mc^2. Mass can be expressed as energy and vice versa through this simple equation. Just plug in the mass and use the speed of light (299,792,458 m/s) to find the energy in Joules (units are kg•m^2/s^2).

E=mc^2
E=1.67x10^-27*(299,792,458)^2
E=1.5x10^-10 J

b) To convert that value to eV, simply use the conversion 1 ev = 1.602176487x10^-19 J to convert:

1.5x10^-10 J / 1.602176487x10^-19 J/eV = 936,801,383 eV.

To check our answer, we can use the values in your hint:

mass = 1.008665*u
mass = 1.008665*939.49x10^6 eV (1 MeV = 10^6 eV)
mass = 947,630,681 eV

Pretty close to our calculated value.. Percent error is only 1.1%, so it's close enough haha.

Answer 2

Thank you :) Can you help me with another one please? :)