Compare the radii of two nuclei with mass numbers 1 and 27 respectively.

1

(a)

\(\frac { { R }_{ 1 } }{ { R }_{ 2 } } ={ \left( \frac { { A }_{ 1 } }{ { A }_{ 2 } } \right) }^{ { 1 }/{ 3 } }={ \left( \frac { 1 }{ 27 } \right) }^{ { 1 }/{ 3 } }=\frac { 1 }{ 3 } \)

In a particular fission reaction, a \(_{ 92 }{ { U }^{ 235 } }\) nucleus captures a slow neutron. The fission products are three neutrons, a \(_{ 57 }{ La^{ 142 } }\)nucleus and a fission product \(_{ Z }{ { X }^{ A } }\). What is the value of Z?

1

(a)

Applying the principle of conservation of charge number. 
\(Z+57=92 \)
\( \therefore \ Z=92-57=35\)

In a typical nuclear reaction e.g
\(_{ 1 }^{ 2 }{ H+_{ 1 }^{ 2 }H{ \longrightarrow _{ 2 }^{ 3 }{ He } }+n+3.27MeV }\)
although number of nucleons is conserved,yet energy is released.How?Explain.

1

(a)

Since the total initial mass of nuclei on the left side of reaction is greater than the total final mass of nucleus on the right hand side,this difference of mass appears as the energy released.

What characteristic property of nuclear force explain the constancy of binding energy per nucleon (BE/A) in the range of mass number 'A' lying 30

1

(a)

Saturation/Short nature of nuclear force

Two nuclei have mass numbers in the ratio 1:8.What is the ratio of their nuclear radii?

1

(a)

\(R={ R }_{ 0 }{ A }^{ 1/3 },{ R }_{ 1 }/{ R }_{ 2 }={ A }_{ 1 }^{ 1/3 }/{ A }_{ 2 }^{ 1/3 }=1,^{ 1/3 }/27_{ 1/3 }=1/3\)