A proton and a deuteron are initially at rest | vedclass

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(B) The kinetic energy $K$ gained by a particle of charge $q$ accelerated through a potential difference $V$ is given by $K = qV$. Since both the prot

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They have same momentum

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(B) The kinetic energy $K$ gained by a particle of charge $q$ accelerated through a potential difference $V$ is given by $K = qV$. Since both the proton and deuteron have the same charge $e$, they both gain the same kinetic energy: $K_p = K_d = eV$. Thus, option $C$ is true.Since $K = \frac{p^2}{2m}$, the momentum $p = \sqrt{2mK}$. Since $m_d = 2m_p$, the momentum of the deuteron $p_d = \sqrt{2(2m_p)eV} = 2\sqrt{m_p eV}$ and the momentum of the proton $p_p = \sqrt{2m_p eV}$. Thus, $p_d = \sqrt{2} p_p$. Therefore, they do not have the same momentum, making option $B$ false.Since $K = \frac{1}{2}mv^2$, $v = \sqrt{\frac{2K}{m}}$. Since $m_d > m_p$, $v_p > v_d$. Thus, they have different speeds, making option $A$ true.The force $F = qE$. Since the electric field $E$ depends on the geometry of the setup and the potential difference, if they are accelerated through the same potential difference in the same field, they experience the same force $F = eE$. However, the statement 'they have been subjected to same force' is often contextually interpreted in these problems as a comparison of their final states or dynamics. Given the options, $B$ is the most fundamentally incorrect statement regarding their physical properties.

$A$ proton and a deuteron are initially at rest and are accelerated through the same potential difference. Which of the following is false concerning the final properties of the two particles?

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