What potential difference is needed to accelerate a

Asked by maham237 @ 17/02/2021 in Physics viewed by 264 People

What potential difference is needed to accelerate a he+ ion (charge +e, mass 4u) from rest to a speed of 1.0×106 m/s ? express your answer using two significant figures?

Answered by maham237 @ 17/02/2021

For the law of conservation of energy, the loss in potential energy of the He+ ion should be equal to the gain in kinetic energy:
$-\Delta U=\Delta K$
which can be rewritten as
$-q \Delta V = \frac{1}{2}mv^2$
where
$q=+e = 1.6 \cdot 10^{-19}C$ is the charge of the ion,
$m=4u=4\cdot 1.67 \cdot 10^{-27}kg$ is the mass of the ion,
$v=1.0 \cdot 10^6 m/s$ is the speed of the ion.
By using these values, we find the potential difference needed:
$\Delta V = \frac{1}{2} \frac{mv^2}{-q}= \frac{1}{2} \frac{(4\cdot 1.67 \cdot 10^{-27}kg)(1.0 \cdot 10^6 m/s)^2}{-1.6 \cdot 10^{-19}C}= -20875 V=-21 kV$
and the negative sign means the final point is at lower voltage than the initial point, and this is correct, because the ion has positive charge and a positive charge travels naturally from higher voltages to lower voltages.

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