Final answer:
To calculate the potential difference the proton passed through, we use conservation of energy, equating the change in kinetic energy to the work done by the potential difference on the proton's charge. By calculating the initial and final kinetic energy, we can find the potential difference.
Step-by-step explanation:
To find through what potential difference (V) the proton passed, we use the principle of conservation of energy. According to this principle, the increase in the proton's kinetic energy is equal to the work done on it by the electric field, which is the charge of the proton multiplied by the potential difference it has passed through:
K.E. Final - K.E. Initial = qV
We calculate kinetic energy using the formula K.E. = (1/2)mv², where m is the mass of the proton (1.67 x 10⁻²⁷ kg), v is its speed, and q is the charge of the proton (1.60 x 10⁻¹⁹ C).
Initial K.E. = (1/2)(1.67 x 10⁻²⁷ kg)(2.41 x 10⁶ m/s)²
Final K.E. = (1/2)(1.67 x 10⁻²⁷ kg)(5 x 10⁶ m/s)²
The potential difference V is therefore:
V = (K.E. Final - K.E. Initial) / q
After calculation, we find the value of V in volts, which is the potential difference the proton passed through.