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

Options

A. `M_2 gt 2M_1`
B. `M_2 lt 2M_1`
C. `M_1 lt 10 (m_n + m_p)`
D. `M_2= 2M_1`

Answer

B

Explanation

The mass of a nucleus is always less than the sum of the masses of its constituent particles . This is due to mass defect. In the case of `""_10Ne^20` atoms, there are 10 protons and 10 neutron.
`therefore M_1 lt 10 (m_p + m_n) " or " (m_p + m_n) gt M_1`
Similarly for `""_20Ca^40, 20 (m_n + m_p) gt M_2`
`therefore` Mass defect = 20 `(m_n +m_p) - M_2`
It is found that the mass defect increases with increase in mass number.
`therefore 20 (m_n + m_p) - (M_2 gt 10 (m_p + m_n) - M_1`
`therefore 10(m_n + m_p) gt (M_2 - M_1)`
`therefore M_1 + 10 (m_n + m_p) gt M_2`
i.e. `M_2 lt M_1 + 10 (m_n + m_p)`
but `M_1 lt 10 (m_n + m_p)`
`therefore M_2 lt 2M_1`