Nuclei Test

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Nuclei Test - 46

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Weekly Quiz Competition

Question 1
1 / -0

Which symbol is used to represent the unit of atomic mass, amu?

A
u

B
A

C
M

D
n

Solution

The symbol 'u' represents the unit of atomic mass, amu. For example, the atomic mass of carbon-12 is written as 12 u.
Hence, option A is correct.
Question 2
1 / -0

A nuclear transformation is denoted by $$X(n, \alpha) \rightarrow _{3}^{7}Li$$. Which of the following is the nucleus of element $$X$$?

A
$$_{6}^{12}C$$

B
$$_{5}^{10}B$$

C
$$_{5}^{9}B$$

D
$$_{4}^{11}Be$$

Solution

$$\begin{aligned}& X(n, \alpha) \longrightarrow{ }_{3}^{7} L_{i} \\X &+n \quad \longrightarrow \quad{ }_{3}^7 L_{i}+\alpha \\\alpha &={ }_2^{4} H_{e}\\n&=^0n\end{aligned}$$

$$\begin{array}{l}X+{ }^{1} n \longrightarrow _{3}^{7} Li+{ }^{4}_2 H_{e} \\X \text { must have Atomic mass }=10\end{array}$$
$$\text { and Atomic no. }=5$$

$${ }^{10}_5 X={ }^{10}_5 B$$
Question 3
1 / -0

The binding energies per nucleon of deuteron $$(_{1}H^{2})$$ and helium atom $$(_{2}He^{4})$$ are $$1.1\ MeV$$ and $$7\ MeV$$. If two deuteron atoms react to form a single helium atom, then the energy released is

A
$$13.9\ MeV$$

B
$$26.9\ MeV$$

C
$$23.6\ MeV$$

D
$$19.2\ MeV$$

Solution

ATQ, following reaction takes place,
$${ H }_{ 1 }^{ 2 }+{ H }_{ 1 }^{ 2 }\rightarrow { H }_{ 2 }^{ 4 }\quad -Q$$
{-Q: energy reloaded}
$$\rightarrow 2({ H }_{ 1 }^{ 2 })\rightarrow { H }_{ 2 }^{ 4 }\quad -Q\\ $$
So, ATQ binding energy per nucleon of deuteron=1.1MeV.
Therefore, There are 2 nucleon in deuteron atom, hence total binding energy
$$=1.1\times 2\\ =2.2MeV$$
Therefore, for left hand part, BE of
$${ H }_{ 1 }^{ 2 }=2.2MeV$$
Similarly, BE per nucleon of helium atom= 7eV.
Number of nucleons in helium$$=4$$
Total BE of nucleus$$==7\times 4=28MeV$$
Now, substituting the values of BE in the equation to get the value of Q,
$$\Rightarrow 2(2.2)\rightarrow 28-Q\\ \rightarrow Q=28-4.4=23.6MeV$$
Question 4
1 / -0

A radioactive nuclide X decays into nuclei T and Z by simultaneous disintegration as shown. Effective decay constant for the disintegration is

A
$${ \lambda }_{ 1 }+{ \lambda }_{ 2 }$$

B
$$\dfrac { { \lambda }_{ 1 }{ \lambda }_{ 2 } }{ { \lambda }_{ 1 }+{ \lambda }_{ 2 } }$$

C
$$\dfrac { { \lambda }_{ 1 }+{ \lambda }_{ 2 } }{ 2 }$$

D
$$\dfrac { 2{ \lambda }_{ 1 }{ \lambda }_{ 2 } }{ { \lambda }_{ 1 }+{ \lambda }_{ 2 } }$$

Solution

$$\begin{array}{l}\frac{d y}{d t}=\lambda_{1} x---\text { for } x \rightarrow y \\\frac{d z}{d t}=\lambda_{2} x--- \text { for } x \rightarrow z \\\text { Now adding }\\\left(\lambda_{1}+\lambda_{2}\right) x=\frac{d y}{d t}+\frac{d z}{d t}\longrightarrow(i) \\\frac{d y}{d t}+\frac{d z}{d t}=-\frac{d x}{d t}\longrightarrow\text { (iii) }\end{array}$$

$$\begin{array}{l}\text { Rate of decrease of } x \\\text { Would be equal to } \\\text { net increase rale } \\\text { of } y \text { and } z \text { . } \\-\frac{d x}{d t}=\left(\lambda_1+\lambda_{2}\right)x\\\Rightarrow \lambda_{\text {effective }}=\lambda_{1}+\lambda_{2}\end{array}$$
Question 5
1 / -0

Decreasing order of atomic weight is correct of the elements given below?

A
$$Fe > Co > Ni$$

B
$$Ni > Co > Fe$$

C
$$Co > Ni > Fe$$

D
$$Co > Fe > Ni$$

Solution

Atomic weight of Iron $$\approx 56$$ u
Atomic weight of Cobalt $$\approx 59$$ u
Atomic weight of Nickel $$\approx 58.7$$ u
So, the order of atomic weights is $$Co>Ni>Fe$$.
Option $$C$$ is correct.
Question 6
1 / -0

A collective name for nucleons and other elementary particles that decay into nucleons by the emission of mesons is?

A
Baryon

B
Boson

C
Fermion

D
Hadron

Solution

$$\begin{array}{l}\text { A collective name for } \\\text { nucleons and other elementry } \\\text { particles that decay into } \\\text { nucleons by the emission } \\\text { of mesons is Hadron. }\end{array}$$
Question 7
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The mass of $$_{ 17 }{ { CI }^{ 35 } }$$ is $$34.9800$$ amu. Calculate its binding energy (mass of $$_{ 0 }{ { n }^{ 1 } }=1.008665$$ amu $$_{ 1 }{ { H }^{ 1 } }=1.007825$$ amu):

A
$$2.88 MeV$$

B
$$28.8 MeV$$

C
$$280 MeV$$

D
$$2880 MeV$$

Solution

There are 17 protons and 18 neutrons in the nucleus of chlorine
$$\Delta$$ m=Mass of the nucleons combined- Actual mass of the nucleus
$$=17\times 1.0007825+18\times 1.0086-34.9800$$
$$=35.288995-34.98$$
$$=0.308995$$
B.E.$$=\Delta m(931.5)=279.45$$
Question 8
1 / -0

The relation between the volume $$V$$ and the mass $$M$$ of a nucleus is:

A
$$V\propto M^{3}$$

B
$$V\propto M^{1/3}$$

C
$$V\propto M$$

D
$$V\propto 1/M$$

Solution

Since the density of nucleus is fixed.
$$D=\cfrac { M }{ V } \\ \Rightarrow M=DV\\ M\propto V$$
Question 9
1 / -0

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:
(i) $$A+B\rightarrow C+\varepsilon $$
(ii) $$C\rightarrow A+B+\varepsilon $$
(iii) $$D+E\rightarrow F+\varepsilon $$
(iv) $$F\rightarrow D+E+\varepsilon $$
where $$\varepsilon $$ is the energy released? In which reactions is $$\varepsilon $$ positive.

A
(ii) and (iv)

B
(ii) and (iii)

C
(i) and (iv)

D
(i) and (iii)

Solution

In a spontaneous reaction product has always Binding energy greater than that of reactants. So, (i) is a fusion reaction and (iv) is a fission reaction.
Question 10
1 / -0

A nucleus of mass $$M+\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $$\cfrac{M}{2}$$ 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
$${ E }_{ 1 }=2{ E }_{ 2 }$$

Solution

$$ \begin{array}{l} \text { let } x \rightarrow 2 y \\ \text { mass } \rightarrow M+\Delta m \quad 2 \times \frac{M}{2}=M \\ \Delta m \text { mass is lost as energy } \\ \Rightarrow \text { energy is released } \\ \Rightarrow \text { energy of } x>\text { energy of y } \\ \qquad E_{1}>E_{2} \\ \text { option } B \end{array} $$

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Re-Attempt Weekly Quiz Competition

Nuclei Test - 46

Result

Nuclei Test - 46

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Rank

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SHARING IS CARING

Question 1

u

A

M

n

Solution

Question 2

$$_{6}^{12}C$$

$$_{5}^{10}B$$

$$_{5}^{9}B$$

$$_{4}^{11}Be$$

Solution

Question 3

$$13.9\ MeV$$

$$26.9\ MeV$$

$$23.6\ MeV$$

$$19.2\ MeV$$

Solution

Question 4

$${ \lambda }_{ 1 }+{ \lambda }_{ 2 }$$

$$\dfrac { { \lambda }_{ 1 }{ \lambda }_{ 2 } }{ { \lambda }_{ 1 }+{ \lambda }_{ 2 } }$$

$$\dfrac { { \lambda }_{ 1 }+{ \lambda }_{ 2 } }{ 2 }$$

$$\dfrac { 2{ \lambda }_{ 1 }{ \lambda }_{ 2 } }{ { \lambda }_{ 1 }+{ \lambda }_{ 2 } }$$

Solution

Question 5

$$Fe > Co > Ni$$

$$Ni > Co > Fe$$

$$Co > Ni > Fe$$

$$Co > Fe > Ni$$

Solution

Question 6

Baryon

Boson

Fermion

Hadron

Solution

Question 7

$$2.88 MeV$$

$$28.8 MeV$$

$$280 MeV$$

$$2880 MeV$$

Solution

Question 8

$$V\propto M^{3}$$

$$V\propto M^{1/3}$$

$$V\propto M$$

$$V\propto 1/M$$

Solution

Question 9

(ii) and (iv)

(ii) and (iii)

(i) and (iv)

(i) and (iii)

Solution

Question 10

$${ E }_{ 2 }>2{ E }_{ 1 }$$

$${ E }_{ 1 }>{ E }_{ 2 }$$

$${ E }_{ 2 }>{ E }_{ 1 }$$

$${ E }_{ 1 }=2{ E }_{ 2 }$$

Solution

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