Final answer:
To find the potential difference needed to accelerate a He ion to a specific speed, one should use the kinetic energy formula and the work-energy principle, calculating V = (1/2)mv^2 / q, with given mass, charge, and the final speed of the ion.
Step-by-step explanation:
The potential difference needed to accelerate a He+ ion (charge e, mass 4 u) from rest to a speed of 2.0×106 m/s can be calculated using the work-energy principle. The kinetic energy (KE) of the ion after acceleration is given by KE = (1/2)mv2, where m is the mass of the ion and v is the final speed. The work done by the electric field is equal to the change in kinetic energy, which can also be expressed as Work = qV, where q is the charge of the ion and V is the potential difference. By setting Work equal to KE, we can solve for the potential difference as V = (1/2)mv2 / q.
Using the given charge of the He ion as 2e (since a He ion would typically have a charge of 2e) and the atomic mass unit (u) which is equal to 1.6605×10-27 kg per u, the potential difference can be calculated accordingly:
V = (1/2)×(4u)×(2.0×106 m/s)2 / (2e)
Substituting the values for u and e gives us the numerical result for the potential difference required.