 JEE Mains Previous Years Questions with Solutions

4.5
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1

AIEEE 2007

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?
A
$n = 1$ to $n=2$
B
$n = 2$ to $n=6$
C
$n = 6$ to $n=2$
D
$n = 2$ to $n=1$

Explanation

We have no find the frequency of emitted photons. For emission of photons the transition must take place from a higher energy level to a lower energy level which are given only in options $(c)$ and $(d)$.

Frequency is given by

$hv = - 13.6\left( {{1 \over {n_2^2}} - {1 \over {n_1^2}}} \right)$

For transition from $n=6$ to $n=2,$

${v_1} = {{ - 13.6} \over h}\left( {{1 \over {{6^2}}} - {1 \over {{2^2}}}} \right)$

$= {2 \over 9} \times \left( {{{13.6} \over h}} \right)$

For transition from $n=2$ to $n=1,$

${v_2} = {{ - 13.6} \over h}\left( {{1 \over {{2^2}}} - {1 \over {{1^2}}}} \right)$

$= {3 \over 4} \times \left( {{{13.6} \over h}} \right).$

$\therefore$ ${v_1} > {v_2}$
2

AIEEE 2007

The half-life period of a ratio-active element $X$ is same as the mean life time of another ratio-active element $Y.$ Initially they have the same number of atoms. Then
A
$X$ and $Y$ decay at same rate always
B
$X$ will decay faster than $Y$
C
$Y$ will decay faster than $X$
D
$X$ and $Y$ have same decay rate initially

Explanation

According to question,

Half life of $X,\,{T_{1/2}} = {\tau _{av}},\,\,\,$ average life of $Y$

$\Rightarrow {{0.693} \over {{\lambda _X}}} = {1 \over {{\lambda _Y}}} \Rightarrow {\lambda _X} = \left( {0.693} \right).{\lambda _Y}$

$\therefore$ ${\lambda _X} < {\lambda _Y}.$

Now, the rate of decay is given by

$- {{dN} \over {dt}} = \lambda N$

$\therefore$ $Y$ will decay faster than $X.$ [ as $N$ is same ]
3

AIEEE 2007

In gamma ray emission from a nucleus
A
only the proton number changes
B
both the neutron number and the proton number change
C
there is no change in the proton number and the neutron number
D
only the neutron number changes

Explanation

There is no change in the proton number and the neutron number as the $\gamma$ - emission takes place as a result of excitation or de-excitation of nuclei. $\gamma$-rays have no charge or mass.
4

AIEEE 2007

If ${M_O}$ is the mass of an oxygen isotope ${}_8{O^{17}}$ , ${M_p}$ and ${M_N}$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is
A
$\left( {{M_O} - 17{M_N}} \right){C^2}$
B
$\left( {{M_O} - 8{M_P}} \right){C^2}$
C
$\left( {{M_O} - 8{M_P} - 9{M_N}} \right){C^2}$
D
${{M_O}{c^2}}$

Explanation

Binding energy

$= \left[ {Z{M_p} + \left( {A - Z} \right){M_N} - M} \right]{c^2}$

$= \left[ {8{M_p} + \left( {17 - 8} \right){M_N} - M} \right]{c^2}$

$= \left[ {8{M_p} + 9{M_N} - M} \right]{c^2}$

$= \left[ {8{M_p} + 9{M_N} - {M_O}} \right]{c^2}$