### JEE Mains Previous Years Questions with Solutions

4.5
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1

### AIEEE 2011

Energy required for the electron excitation in $L{i^{ + + }}$ from the first to the third Bohr orbit is :
A
$36.3$ $eV$
B
$108.8$ $eV$
C
$122.4$ $eV$
D
$12.1$ $eV$

## Explanation

Energy of excitation,

$\Delta E = 13.6\,{Z^2}\left( {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right)eV$

$\Rightarrow \Delta E = 13.6{\left( 3 \right)^2}\left( {{1 \over {{1^2}}} - {1 \over {{3^2}}}} \right) = 108.8\,eV$
2

### AIEEE 2010

A radioactive nucleus (initial mass number $A$ and atomic number $Z$ emits $3\,\alpha$- particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
A
${{A - Z - 8} \over {Z - 4}}$
B
${{A - Z - 4} \over {Z - 8}}$
C
${{A - Z - 12} \over {Z - 4}}$
D
${{A - Z - 4} \over {Z - 2}}$

## Explanation

${}_Z^AX\mathop \to \limits^{A - 12} {}_{Z - 8}Y + 3{}_2^4{X_e} + {}_t^0e$

Number of protons, Np = Z - 8

Number of neutrons, Nn = $A - 12 - \left( {Z - 8} \right)$

$\therefore$ Required ratio $= {{A - Z - 4} \over {Z - 8}}$
3

A nucleus of mass $M+$$\Delta m is at rest and decays into two daughter nuclei of equal mass {M \over 2} each. Speed of light is c. The speed of daughter nuclei is A c{{\Delta m} \over {M + \Delta m}} B c\sqrt {{{2\Delta m} \over M}} C c\sqrt {{{\Delta m} \over M}} D c\sqrt {{{\Delta m} \over {M + \Delta m}}} ## Explanation By conservation of energy, \left( {M + \Delta m} \right){c^2} = {{2M} \over 2}{c^2} + {1 \over 2}.{{2M} \over 2}{v^2}, where v is the speed of the daughter nuclei \Rightarrow \Delta m{c^2} = {M \over 2}{v^2} \therefore v = c\sqrt {{{2\Delta m} \over M}} 4 ### AIEEE 2010 MCQ (Single Correct Answer) A nucleus of mass M+$$\Delta m$ is at rest and decays into two daughter nuclei of equal mass ${M \over 2}$ each. Speed of light is $c.$

The binding energy per nucleon for the parent nucleus is ${E_1}$ and that for the daughter nuclei is ${E_2}.$ Then

A
${E_2} = 2{E_1}$
B
${E_1} > {E_2}$
C
${E_2} > {E_1}$
D
${E_1} = 2{E_2}$

## Explanation

In nuclear fission, the binding energy per nucleon of daughter nuclei is greater than the parent nucleon of daughter nuclei is greater than the parent nucleus.