Question

Physicists often use a different unit of energy, the electron volt, when dealing with energies at the atomic level. One electron volt, abbreviated eV, is defined as the amount of kinetic energy gained by an electron upon accelerating through a 1.0 V potential difference.
a) what is 1.0 electron volt in joules?

b) what is the speed of a proton with 5000 eV of kinetic energy?

Answer 1

Answer:

a)  E = 1.06 10⁻¹⁹ J,     b)   v = 9.78 10⁵ m / s

Explanation:

The physical magnitudes can be given in several units, but in general all must be reduced to the same system in a given exercise, the most used system is the international (SI)

           1 eV =q V=  1.6 10⁻¹⁹ J

let's reduce the quantities requested

a) E = 1.0 eV to Joule

           E = 1.0 eV (1.6 10⁻¹⁹ J / 1 eV)

           E = 1.06 10⁻¹⁹ J

b) the kinetic energy is given by

           K = ½ m v²

           v = $\sqrt{\frac{2K}{m} }$

the mass of the proton is

          m = 1,673 10⁻²⁷ kg

let's reduce the energy to the SI system

           E = 5000 ev (1.6 10-19 J / 1 eV) = 8000 10⁻¹⁹ J

let's calculate

           v = $\sqrt{ \frac{2 \ 8000 \ 10^{-19}}{1.673 \ 10^{-27} } }$

           v = $\sqrt{ 95.637 \ 10^{10} }$

           v = 9.78 10⁵ m / s