Calculate the ratio of de-Broglie wavelengths associated with a deutron moving with velocity 2v and an alpha particle moving with velocity v.

Explanation

Deutron is a particle having one proton and one neutron. Hence mass of deutron =twice the mass of nucleon=`2m_p`. Alpha particle is a particle having two protons and two neutrons. Hence mass of alpha particle=four time the mass of nucleon `=4m_p`
De-Broglie wavelength association with deutron moving with velocity 2v is
`lambda_1=h/(2m_pxx2v)=h/(4m_pv)....(i)`
de-Broglie wavelength associated with alpha particle moving with the velocity v is
`lambda_2=h/(4m_pv)......(ii)`
`:. (lambda_1)/(lambda_2)=1 or lambda_1:lambda_2=1:1`