An α-particle and a proton are accelerated through same potential difference

An α-particle and a proton are accelerated through same potential difference from rest. Find the ratio of their final velocity

(a) (4:1)
(b) (1:1)
(c) (1:√2)
(d) (1:2)

(1:√2)

When a charged particle of charge q and mass m is accelerated from rest through a potential difference V.

.·. Gain in kinetic energy = Loss in potential energy

(1/2) mv² – (1/2) m(0)² = qV or (1/2) mv² = qV or v = √(2qV / m)

For proton, v(p) = √[2eV / m(p)] = √[2eV / m] —–(i)

where m is the mass in atomic mass unit

For α-particle v(α) = √[2(2e)V / m(α)]

= √[2(2e)V / 4m] = (1/√2) v(p)

Therefore, v(α) / v(p) = 1/√2

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