If helium nuclei and protons are each accelerated from rest through the same potential difference, how do the resulting speeds compare?

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Quizplus · Accepted Answer

When particles are accelerated through the same potential difference, their kinetic energy gained is equal to the charge of the particle times the potential difference. Since the charge of a helium nucleus (alpha particle) is twice that of a proton, it gains twice the energy. However, a helium nucleus has four times the mass of a proton. The relationship between kinetic energy (K.E.) and velocity (v) is given by K.E. = 1/2 mv^2, where m is mass. For the same kinetic energy, a particle with a larger mass will have a lower velocity. Thus, when you solve for the velocities using the kinetic energy formula, taking into account the mass and charge differences, you find that protons, being lighter, will attain a higher speed than helium nuclei. The exact factor depends on the square root of the mass ratio, which leads to the protons attaining a speed approximately 1.4 times that of the helium nuclei.

If Helium Nuclei and Protons Are Each Accelerated from Rest