The ratio of the accelerating potentials required to accelerate (i) an -particle and (ii) a proton to have the same de Broglie wavelength associated with them is (mass of - particle = 6.4 10⁻²⁷ kg, mass of proton = 1.6 10⁻²⁷ kg)

Step-by-step solution

The de Broglie wavelength is given by = h 2mqV . Since the de Broglie wavelengths are the same, _ = _ p . h 2m_ q_ V_ = h 2m_ p q_ p V_ p m_ q_ V_ = m_ p q_ p V_ p V_ V_ p = m_ p q_ p m_ q_ Given m_ = 6.4 10⁻²⁷ kg and m_ p = 1.6 10⁻²⁷ kg, we have m_ = 4m_ p . The charge of an -particle is twice that of a proton, so q_ = 2q_ p . V_ V_ p = m_ p q_ p 4m_ p 2q_ p = 1 8 The ratio is 1 : 8 . Answer: 1 : 8