 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2003

If the binding energy of the electron in a hydrogen atom is $13.6eV,$ the energy required to remove the electron from the first excited state of $L{i^{ + + }}$ is
A
$30.6$ $eV$
B
$13.6$ $eV$
C
$3.4$ $eV$
D
$122.4$ $eV$

Explanation

${E_n} = - {{13.6} \over {{n^2}}}{Z^2}eV/$atom

For lithium ion $Z=3;$ $n=2$ (for first excited state)

${E_n} = - {{13.6} \over {{2^2}}} \times {3^2} = - 30.6eV$
2

AIEEE 2003

Which of the following cannot be emitted by radioactive substances during their decay ?
A
Protons
B
Neutrinoes
C
Helium nuclei
D
Electrons

Explanation

The radioactive substances emit $\alpha$ -particles (Helium nucleus), $\beta$ -particles (electrons) and neutrinoes.
3

AIEEE 2003

In the nuclear fusion reaction $${}_1^2H + {}_1^3H \to {}_2^4He + n$$
given that the repulsive potential energy between the two nuclei is $\sim 7.7 \times {10^{ - 14}}J$, the temperature at which the gases must be heated to initiate the reaction is nearly
[ Boltzmann's Constant $k = 1.38 \times {10^{ - 23}}\,J/K$ ]
A
${10^7}\,\,K$
B
${10^5}\,\,K$
C
${10^3}\,\,K$
D
${10^9}\,\,K$

Explanation

The average kinetic energy per molecule $= {3 \over 2}kT$

This kinetic energy should be able to provide the repulsive potential energy

$\therefore$ ${3 \over 2}kT = 7.7 \times {10^{ - 14}}$

$\Rightarrow T = {{2 \times 7.7 \times {{10}^{ - 14}}} \over {3 \times 1.38 \times {{10}^{ - 23}}}} = 3.7 \times {10^9}$
4

AIEEE 2003

The wavelengths involved in the spectrum of deuterium $\left( {{}_1^2\,D} \right)$ are slightly different from that of hydrogen spectrum, because
A
the size of the two nuclei are different
B
the nuclear forces are different in the two cases
C
the masses of the two nuclei are different
D
the attraction between the electron and the nucleus is different in the two cases

Explanation

The wavelength of spectrum is given by

${1 \over \lambda } = R{z^2}\left( {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right)$

where $R = {{1.097 \times {{10}^7}} \over {1 + {m \over M}}}$

where $m=$ mass of electron

$M=$ mass of nucleus.

For different $M,R$ is different and therefore $\lambda$ is different