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

a) 1.0 electron volt (eV) is equal to 1.60 × 10^(-19) joules (J). b) The speed of a proton with 5000 eV of kinetic energy is approximately 1.19 × 10^7 m/s.

Step-by-step explanation:

a) To convert 1 electron volt (eV) to joules (J), we can use the conversion factor 1 eV = 1.60 × 10-19 J (as given in the reference information). Therefore, 1.0 eV is equal to 1.60 × 10-19 J.

b) The kinetic energy of a proton with 5000 eV can be calculated using the equation E = 0.5mv2, where E is the kinetic energy, m is the mass of the proton, and v is its velocity. Since we are given the energy in eV, we need to convert it to joules before proceeding. Using the conversion factor 1 eV = 1.60 × 10-19 J, we can convert 5000 eV to 8.00 × 10-17 J. Now we can plug this value into the equation along with the mass of a proton (1.67 × 10-27 kg) to find the velocity of the proton. Solving for v, we get v = √(2E/m) = √(2(8.00 × 10-17 J)/(1.67 × 10-27 kg)) ≈ 1.19 × 107 m/s.