Question

An Alpha particle and proton are accelerated at the same potential difference calculate the ratio of velocities acquired by the two particles.

Answer 1

Answer:

Explanation:

The two particles will gain a certain amount of energy from the electric field, Eproton and Ealpha. Let's (arbitrarily) choose to measure that energy in electron-volts rather than in the usual Joules. Straight way, we see that Ealpha=2*Eproton, since it carries twice the electric charge.

Now, let's divide each by half the mass, and take the square-root (since E=½MV²), that gives Valpha=√(2*Ealpha/Malpha) and Vproton=√(2*Eproton/Mproton).

But, we saw that Ealpha=2*Eproton, and we know that Malpha=4*Mproton (approximately, anyway).

So, we have Vproton/Valpha = √((Eproton/Mproton)/(2*Eproton/4*Mproton)) which is √(4/2) , namely √2, or about 1.414.

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