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 electron volt in joules? b. What is the speed of a proton with 5000 eV of kinetic energy?

Short answer

(a) 1.0 electron volt in joules is$1.6\times {10}^{-19}J$.

(b) The speed of a proton with 5000 eV of kinetic energy is$9.8\times {10}^{5}m/s.$

Step-by-step solution

Step 1. Given information

Physicists often use a different unit of energy, the electron volt, when dealing with energies at the atomic level.

We need to find a). What is 1 electron volt in joules?

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

Step 2. Finding the 1 electron volt in joules.

(a) By the definition provided, we have

$1\mathrm{eV}=1.6·{10}^{-19}\mathrm{C}·1\mathrm{V}=1.6·{10}^{-19}\mathrm{J}$

Step 2. Finding the energy

(b) an energy$5\mathrm{keV}$will correspond to

$E=5\mathrm{keV}=5·{10}^3·1.6·{10}^{-19}=\underset{¯}{8·{10}^{-16}\mathrm{J}}$

We can thus find the speed to be

$E=\frac{m{v}^2}{2}\Rightarrow v=\sqrt{\frac{2E}{m}}$

We numerically have

$v=\sqrt{\frac{2·8·{10}^{-16}}{1.67·{10}^{-27}}}=9.8·{10}^5\mathrm{m}/\mathrm{s}$