A proton is accelerated by a uniform electric field - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 4

To determine the time required for the helium nucleus to achieve the same change in speed as the proton, we begin by recognizing that the acceleration ($a$) of an object in an electric field ($E$) is given by the equation:

$a = \frac{F}{m} = \frac{qE}{m}$

where $F$ is the force acting on the charge, $q$ is the charge, and $m$ is the mass of the particle.

For a proton, with charge $e$ and mass $m_p$, the acceleration is:

$a_p = \frac{eE}{m_p}$

For the helium nucleus, which has twice the charge ($2e$) and four times the mass ($4m_p$), the acceleration will be:

$a_{He} = \frac{2eE}{4m_p} = \frac{eE}{2m_p} = \frac{1}{2}a_p$

Since the acceleration of the helium nucleus $a_{He}$ is half that of the proton, it will take twice as long to achieve the same change in speed as the proton. If the proton achieves a change in speed $riangle v$ in time $t$, the helium nucleus will require:

$t_{He} = 2t$

In the context of the provided options, since the options are relative to the change in speed of the proton after time $t$, we conclude:

Therefore, the answer is:

B) 2t