Final answer:
To calculate the voltage necessary to accelerate protons from rest to a speed of 2×105 m/s, the work-energy principle is used, where the electric field work equates to the kinetic energy change. With the proton's mass, charge, and desired speed, one can calculate the voltage.
Step-by-step explanation:
To find the magnitude of the voltage necessary to accelerate the protons from rest to a final speed of 2×105 m/s, we can use the work-energy principle which states that the work done on a particle is equal to the change in its kinetic energy. The work done by the electric field in accelerating a proton is equal to the charge of the proton times the potential difference (voltage), and the kinetic energy of a particle is (1/2)mv2 where m is the mass of the proton and v is its velocity.
Since a proton has a mass of 1.67×10-27 kg and the same magnitude of charge as an electron, which is e = 1.60×10-19 C, the formula we use is:
qV = (1/2)mv2
Plugging in the known values:
1.60×10-19 C × V = (1/2)(1.67×10-27 kg)(2×105 m/s)
From this, we can solve for V (the voltage), which gives:
V = ∈(1/2)(1.67×10-27 kg)(2×105 m/s)2 / (1.60×10-19 C)
Performing the calculation yields the voltage necessary for the acceleration of protons.