Final answer:
The potential difference needed to accelerate a helium ion from rest to a speed of 1.8×106 m/s is found by first calculating the kinetic energy using the mass of the ion and its final speed, then dividing this energy by the charge of the ion to find the potential difference.
Step-by-step explanation:
The question asks what potential difference is needed to accelerate a helium ion (He ion), with a charge of +e and a mass of 4u (atomic mass units), from rest to a speed of 1.8×106 m/s. To solve this, we use the work-energy principle that equates the work done by the electric field to the kinetic energy gained by the ion.
First, we find the kinetic energy (KE) of the helium ion using the formula:
KE = (1/2)mv2
Where:
- m is the mass of the helium ion, which we must convert to kilograms. The conversion is as follows: 1u = 1.66×10-27 kg, so for a helium ion of 4u, it would be 4 × 1.66×10-27 kg.
- v is the final speed of the helium ion, which is given as 1.8×106 m/s.
After calculating KE, we determine the potential difference (V) needed to accelerate the helium ion from rest:
V = KE/e
Where e is the elementary charge, 1.60×10-19 C.