An alpha particle and a proton are accelerated from rest through the same potential difference V Find the ratio - Physics - Dual Nature Of Radiation And Matter

Question

An alpha particle and a proton are accelerated from rest through
the same potential difference V Find the ratio of de-Broglie
wavelengths associated with them

B.santhiya · Accepted Answer

The de-Broglie wavelength associated witha
proton having charge e and
accelerated through a potential difference V is
given by
λ = h /( 2mev)1/2 (i)
suppose that α - particle posses the
de-Broglie wavelength λ' , when accelerated
through the same V if e' amd m'
are the values of charge and mass of the α -particle ,
then
λ' = h/(2m'e' V)1/2 (ii)
dividing eqn (i) by (ii) , we have
λ / λ' = h / (2meV)1/2 x (2m'e'
V)1/2 / h
= (m' e' / m e)1/2
as u know , mass of alpha particle is 4 times the proton
and charge is 2 times greater,
m' = 4m ; e' = 2e
therefore
λ / λ ' = (4m x 2e / m e)1/2
= (8)1/2

An alpha particle and a proton are accelerated from rest through the same potential difference V. Find the ratio of de-Broglie wavelengths associated with them.