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Let m(p) be the mass of a poton , M(1) t...

Let `m_(p)` be the mass of a poton , `M_(1)` the mass of a `_(10)^(20) Ne` nucleus and `M_(2)` the mass of a `_(20)^(40) Ca` 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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Knowledge Check

  • 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 = M_1`
    B
    `M_2 gt M_1`
    C
    `M_2 lt M_1`
    D
    `M_1 lt 10 (m_n + m_p)`

  • Let m_(p) , be the mass of a proton, m_(n) , that of a neutron, M_(1) , that of a ""_(10)^(20)Ne nucleus and M_(2) , that of a ""_(20)^(40) Ca nucleus. Then

    A
    `M_(2) = 2M_(1)`
    B
    `M_(1) lt 10(m_(p) + m_(n))`
    C
    `M_(2) gt 2M_(1)`
    D
    `M_(1) = M_(2)`

  • If m_(p) is the mass of proton. m_(n) that of a neutron, M_(1) that of _(10)Ne^(20) nucleus and M_(2) that of _(20)Ca^(40) nucleus, then which of the following relations is//are not true?

    A
    `M_(2) gt 2M_(1)`
    B
    `M_(2) lt 20 (m_(p)+m_(n))`
    C
    `M_(2)=2M_(1)`
    D
    `M_(2) lt 2M_(1)`

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