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Let mp be the mass of a proton , mn the ...

Let `m_p` be the mass of a proton , `m_n` the mass of a neutron, `M_1` the mass of a `._10^20Ne` nucleus and `M_2` the mass of a `._20^40Ca` nucleus . Then

A

`M_(2) = 2 M_(1)`

B

`M_(2) gt 2M_(1)`

C

`M_(2) lt 2M_(1)`

D

`M_(1) lt 10(m_(n) + m_(p))`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Due to mass defect (which is finally responsible for the binding energy of the nucleus), mass of a nucleus is always less than the sum of masses of its constituent particles. `._(1.0)^(20)Ne` is made up of `10` protons plus `10` neutrons.
Therefore, mass of `._(10)^(20)Ne` nucleus,
`M_(1) lt 10 (m_(p)+m_(n))`
Also, heavier the nucleus, more is the mass defect. Thus, `20 (m_(n)+m_(p))-M_(2) gt 10 (m_(p)+m_(n))-M_(1)`
`implies 10 (m_(p)+m_(n)) gt M_(2)-M_(1) implies M_(2) lt M_(1)+10(m_(p)+m_(n))`
Now since `M_(1) lt 10 (m_(p)+m_(n)) :. M_(2) lt 2M_(1)`
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