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1

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

$$ \Rightarrow \Delta m{c^2} = {M \over 2}{v^2}$$

$$\therefore$$ $$v = c\sqrt {{{2\Delta m} \over M}} $$
2

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.
3

AIEEE 2009

MCQ (Single Correct Answer)

The above is a plot of binding energy per nucleon $${E_b},$$ against the nuclear mass $$M;A,B,C,D,E,F$$ correspond to different nuclei. Consider four reactions :
$$\eqalign{ & \left( i \right)\,\,\,\,\,\,\,\,\,\,A + B \to C + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,\,\,\,C \to A + B + \varepsilon \,\,\,\,\,\,\,\,\,\, \cr & \left( {iii} \right)\,\,\,\,\,\,D + E \to F + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,\,\,F \to D + E + \varepsilon ,\,\,\,\,\,\,\,\,\,\, \cr} $$

where $$\varepsilon $$ is the energy released? In which reactions is $$\varepsilon $$ positive?

A
$$(i)$$ and $$(iii)$$
B
$$(ii)$$ and $$(iv)$$
C
$$(ii)$$ and $$(iii)$$
D
$$(i)$$ and $$(iv)$$

Explanation

For $$A + B \to C + \varepsilon ,\,\,\varepsilon $$ is positive. This is because $${E_b}$$

for $$C$$ is greater than the $${E_b}$$ for $$A$$ and $$B$$.

Again for $$F \to D + E + \varepsilon ,\varepsilon $$ is positive. This is

because $${E_b}$$ for $$D$$ and $$E$$ is greater than $${E_b}$$ for $$F.$$
4

AIEEE 2009

MCQ (Single Correct Answer)
The transition from the state $$n=4$$ to $$n=3$$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from :
A
$$3 \to 2$$
B
$$4 \to 2$$
C
$$5 \to 4$$
D
$$2 \to 1$$

Explanation

It is given that transition from the state $$n=4$$ to $$n=3$$ in a hydrogen like atom result in ultraviolet radiation. For infrared radiation the energy gap should be less. The only option is $$5$$ $$ \to 4.$$

Questions Asked from Atoms and Nuclei

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