Arrange the following particles having same velocities in descending…

The correct answer is Option (1) → (C), (B), (A), (D)

The de Broglie wavelength is \( \lambda = h/mv \). For the same velocity, \( \lambda \) is inversely proportional to the mass, so the descending order of wavelength is the ascending order of mass.

    \( \displaystyle \lambda = \frac{h}{mv} \Rightarrow \lambda \propto \frac{1}{m} \)

    \( m_{\text{positron}} = m_e \)
    \( m_{\text{proton}} = m_p \approx 1836\,m_e \)
    \( m_{\text{deuteron}} \approx 2m_p \)
    \( m_{\text{helium nucleus}} \approx 4m_p \)

So the descending order of wavelength is (C), (B), (A), (D).