Nuclei Test

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Nuclei Test - 66

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Weekly Quiz Competition

Question 1
1 / -0

In the uranium radioactive series the initial nucleus is $$_{92} U^{238},$$ and the final nucleus is $$_{82} U^{206}.$$ When the Uranium nucleus decays to lead, the number of $$\alpha-particles$$ emitted are... and the number of $$\beta-particles$$ emitted are...

A
$$6, 8$$

B
$$8, 6$$

C
$$16, 6$$

D
$$32, 12$$

Solution

$$\begin{array}{l}\text { For each. } \alpha \text { -decay Mass number } \\\text { decreases by }{ }^{\prime\prime} 4^{\prime \prime} \text { and } Z \text { by " } 2^{\prime \prime} \\238 \longrightarrow 206\end{array}$$

$$\begin{array}{l}\text { Decrease in mass aumber is }{ }^{\prime\prime} 32^{\prime \prime} \\\text { Let number of }{ }^{\prime \prime} \alpha^{\prime \prime} \text { particles and }\\^{\prime\prime} \beta^{\prime \prime} \text { particles emitted be " } x^{\prime \prime} \text { and "y" } \\\qquad \begin{array}{c}4 x=32\\x=8\end{array}\end{array}$$

$$\begin{array}{l}\therefore \text { No. of } \alpha \text { -particles emitted will be } 8. \\\text { Now, due to this emission } z \text { decrease } \\\text { by } 16. \\\qquad \therefore \quad z=76 \\\quad 76\rightarrow 82 \\\therefore \quad y=6 \\\text { No of } \beta \text { -particles emitted is " } 6 ".\end{array}$$
Question 2
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A radioactive nucleus $$_ZX^A$$ emits $$3 \alpha$$-particles and $$5 \beta$$-particles. The ratio of number of neutron, protons in the product nucleus will be :-

A
$$\dfrac{A-Z-12}{Z-6}$$

B
$$\dfrac{A-Z}{Z-1}$$

C
$$\dfrac{A-Z-11}{Z-1}$$

D
$$\dfrac{A-Z-12}{Z-1}$$

Solution

The new mass number after emission of $$3$$ alpha particles will be $$A-3\times 4=A-12$$
the new atomic number after emission of $$3$$ alpha particles will be $$Z-3\times2=Z-6$$
and after emission of $$5$$ beta particles, this will become $$Z-6 +5\times 1=Z-1$$

so the number of $$neutrons $$ in the new nucleus will be $$A-12-(Z-1)=A-Z-11$$
and the number of $$protons $$ in the new nucleus will be $$(Z-1)$$
the required ration will be $$\dfrac{n}{p}=\dfrac{A-Z-11}{Z-1}$$
Question 3
1 / -0

A nucleus of mass $$M$$ is at rest. An alpha particle of mass $$m$$ is emitted from the nucleus with momentum $$P. Q$$ value of the nuclear reaction is :

A
$$\dfrac {p^{2}M}{2m(M + m)}$$

B
$$\dfrac {p^{2}m}{2m(M + m)}$$

C
$$\dfrac {p^{2}M}{2m(M - m)}$$

D
$$\dfrac {p^{2}m}{2m(M - m)}$$

Solution

$$ \begin{array}{l} \text { Given, } \\ \text { nucleus of mass }=M \\ \text { mass of } \alpha \text { particle }=m \\ \text { momentem of } \alpha \text { -particle }=P \\ \therefore K E \text { of } \alpha \text { panticle }=\dfrac{p^{2}}{2 m} \end{array} $$
$$ \begin{array}{l} \text { We know relation, } \\ \text { when } \alpha \text { paticle decay take place } \\ \qquad(K E)_{\alpha}=Q\left(\dfrac{A-\text { (mass of } \alpha )}{A}\right) \end{array} $$
$$ Q=\dfrac{p^{2} M}{2 m(M-m)} $$
Question 4
1 / -0

$$\begin{array} { l } { \text { Initial ratio of active nuclei in two different samples } } \\ { \text { is } 2 : 3 . \text { Their half lives are } 2 \text { hr and } 3 \text { hr respectively. } } \\ { \text { Ratio of their activities at the end of } 12 \text { hr is: } } \end{array}$$

A
$$1 : 6$$

B
$$6 : 1$$

C
$$1 : 4$$

D
$$4 : 1$$

Solution
Question 5
1 / -0

In which sequence the radioactive radiations are emitted in the following nuclear reaction?
$$_{Z}X^{A} \rightarrow _{Z+1}Y^{A} \rightarrow _{Z-1}K^{A-4} \rightarrow _{Z-1}K^{A-4}$$

A
$$\gamma, \alpha ,\beta$$

B
$$\alpha ,\beta,\gamma$$

C
$$\beta,\gamma,\alpha$$

D
$$\beta,\alpha,\gamma$$

Solution
Question 6
1 / -0

$$\begin{matrix} M \\ Z \end{matrix}A(g)\longrightarrow \begin{matrix} M-B \\ Z-4 \end{matrix}B(g)+(\alpha -particals)$$
($$\alpha$$-particales are helium nuclei,so will form helium gas by trapping electrons)
The radioactive disintegration follows first-order kinetic Starting with 1 mol of A in a 1-litre closed flask at $$27^oC$$ pressure developed after two half-lives is approximately:

A
25 atm

B
12 atm

C
61.5 atm

D
40atm

Solution
Question 7
1 / -0

If the binding energy per nucleon in $$ ^7_3Li and ^4_2 He $$ nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction
$$ p + ^7_3 Li \rightarrow 2^4_2 He $$
energy of proton must be :

A
39.2 MeV

B
28.24 MeV

C
17.28 MeV

D
1.46 MeV

Solution
Question 8
1 / -0

Ratio of energy produced by fusion of 1.0 kg of hydrogen (as it occurs in sun) and energy produced by fission of 1 kg of $$^{235}_{92}{U}$$ in a nuclear reactor is nearly

A
1 : 1

B
2 : 1

C
4 : 1

D
8 : 1

Solution
Question 9
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Two isotopes P and Q of atomic weight 10 and 20, respectively are mixed in equal amount by weight. After 20 days their weight ratio is found to be 1 : 4. Isotope P has a half-life of 10 days. The half-life of isotope Q is

A
zero

B
5 days

C
20 days

D
infinite

Solution

Let Wg of each be taken initid modes of P
$$\begin{array}{l} =\frac { W }{ { 10 } } \\ \emptyset =\frac { W }{ { 20 } } \\ FindP=\frac { { { W_{ 1 } } } }{ { 5\times 10 } } \\ \emptyset =\frac { { 4{ W_{ 1 } } } }{ { 20\times 5 } } \\ \therefore for\, \, { P_{ 1 } }\frac { { W\times 5\times 10 } }{ { 10{ W_{ 1 } } } } ={ \ell ^{ \times P\times 20 } }\to (i) \\ for\, \, \emptyset { { 1pt }_{ 1 } }\frac { { W\times 20\times 5 } }{ { 20\times { W_{ 1 } }\times 4 } } ={ \ell ^{ \lambda \emptyset \times 20 } }\to (ii) \\ from\, \, \left( 1 \right) \, \& \, \, \left( 2 \right) \\ 4{ \ell ^{ \left( { \lambda P-\lambda \emptyset } \right) \times 20 } } \\ 20\left( { \lambda P-\lambda \emptyset } \right) =\log { e^{ 4 } } \\ 20\left( { \frac { { 0.693 } }{ { { t_{ \frac { 1 }{ 2 } } } } } -\frac { { 0.693 } }{ { 10 } } } \right) =\log { e^{ 4 } } \\ { t_{ \frac { 1 }{ 2 } } }=5 \end{array}$$
Question 10
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The nuclear reaction $$1H^2 + 1H^2 \rightarrow 2He^4$$ (mass of $$deuteron=2.0141$$ amu and of $$He=4.0024$$ amu) is

A
fusion reaction releasing 24 MeV energy

B
fusion reaction absorbing 24 MeV energy

C
fission reaction releasing 0.0258 MeV energy

D
fission reaction absorbing 0.0258 MeV energy

Solution