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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2011

MCQ (Single Correct Answer)
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

MCQ (Single Correct Answer)
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

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 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.

Questions Asked from Atoms and Nuclei

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