`M_(1) and M_(2)` represent the masses of `._(10)Ne^(20)` nucleus and `._(20)Ca^(40)` nucleus respectively. State whether `M_(2)=2M_(1)` or `M_(2)gt2M_(1)` or `M_(2)lt2M_(1)`

Answer

`M_(2)>2M_(1)`

Explanation

Let `m_(p)` be the mass of a proton and `m_(n)` be the mass of a neutron. As some energy is required to bind a nucleus, the mass of the nucleus is always less than the mass of constituent nucleons. Therefore,
`M_(1)lt10(m_(p)+m_(n))`
`M_(2)lt20(m_(p)+m_(n))`
As BE/nucleon of `._(20)Ca^(40)` is more than that of `._(10)Ne^(20)`, the factor
`(M_(2)-20(m_(p)+m_(n)))/40gt (M_(1)-10(m_(p)+m_(n)))/20`
or `M_(2)-20(m_(p)+m_(n))gt 40/20[M_(1)-10(m_(p)+m_(n))]`
of `M_(2)gt2M_(1)`