Nuclei Test

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Nuclei Test - 42

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Weekly Quiz Competition

Question 1
1 / -0

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear size will be

A
$$2^{1/3} : 1$$

B
$$1 : 3^{1/2}$$

C
$$3^{1/2} : 1$$

D
$$1:2^{1/3}$$

Solution

Since the linear momentum of the system must be conserved, the total momentum finally after disintegration remains same as that in beginning $$=0$$
$$\implies m_1v_1-m_2v_2=0$$
$$\implies \dfrac{m_1}{m_2}=\dfrac{v_2}{v_1}=\dfrac{1}{2}$$

Since the density of both particles is same,
$$\dfrac{\rho\dfrac{4}{3}\pi r_1^3}{\rho\dfrac{4}{3}\pi r_2^3}=\dfrac{1}{2}$$
$$\implies \dfrac{r_1}{r_2}=\dfrac{1}{2^{1/3}}$$
Question 2
1 / -0

Assume that the nuclear binding energy per nuclear $$(B/A)$$ versus mass number $$(A)$$ as shown in the figure. Use this plot to choose the correct choice (s) given below.

A
Fusion of two nuclei with mass number lying in the range of $$51 < A<100$$ will release energy

B
Fission of a nucleus lying in the mass range of $$200 < A < 260$$ will release energy when broken into two equal fragments

C
Both (a) and (b)

D
None of the above

Solution

Energy will be released when binding energy per nucleon will increase after fusion, here fusion of two nuclei in the range of 51 to 100 will increase to 102 to 200 after fusion as shown in the figure.Hence energy will be released. Similarly in fission of 200 to 260 final mass no becomes 100 to 130.
Hence the answer is option C.
Question 3
1 / -0

Radiocarbon is produced in the atmosphere as a result of

A
collision between fast neutrons and nitrogen nuclei present in the atmosphere

B
action of ultraviolet light from the sun on atmospheric oxygen

C
action of solar radiations particularly cosmic rays on carbon dioxide present in the atmosphere

D
lightning discharge in atmosphere

Solution

Radiocarbon is produced in the atmosphere as result of collision between fast neutrons and nitrogen nuclei present in the atmosphere.
Nuclear reaction is given as :
$$_7N^{14} \ + \ _0n^1 \ \rightarrow \ _6C^{14} \ + \ _1H^1$$
Question 4
1 / -0

Isotopes of an element contain

A
the same number of protons but different number of neutrons

B
the same number of neutrons but different number of protons

C
equal number of protons and electrons

D
equal number of nucleons

Solution

Isotopes of an element must have same atomic number $$(Z)$$ but different mass number $$A$$.
Number of protons is equal to the atomic number.
So, isotopes of an element have same number of protons.
Mass number is equal to the sum of number of protons and neutrons i.e. $$A = p+n$$
As isotopes of an element have different mass number but same number of protons, thus they must have different number of neutrons.
Question 5
1 / -0

The explosion of hydrogen bomb is based on the principle of

A
Uncontrolled fission reaction

B
Nuclear fusion reaction

C
Controlled fission reaction

D
Photoelectric effect

Solution

Nuclear fusion is a reaction in which two or more atomic nuclei come close enough to form one or more different atomic nuclei and subatomic particles (neutrons and/or protons). The difference in mass between the products and reactants is manifested as the release of large amounts of energy.
A hydrogen bomb derives its energy from this type of nuclear reaction.
Question 6
1 / -0

Consider the following statements.
(i) All isotopes of an element have the same number of neutrons.
(ii) Only one isotope of an element can be stable and non-radioactive.
(iii) All elements have isotopes.
(iv) All isotopes of Carbon can form chemical compounds with Oxygen-$$16$$.
The correct option regarding an isotope is$$?$$

A
(iii) and (iv) only

B
(ii), (iii) and (iv) only

C
(i), (ii) and (iii) only

D
(i), (iii) and (iv) only

Solution

All elements have isotopes--atoms of the same element can have different number of neutrons.
Carbon form compounds (carbon monoxide and carbon dioxide) with oxygen. This means that all isotopes of carbon can form compounds (carbon monoxide and carbon dioxide) with all isotopes of oxygen, including oxygen-16.
Question 7
1 / -0

The equation, $$ 4_1H^1 \rightarrow [ _2He^4]^{2+} + 2e^- ; + 26 MeV $$ represents :

A
$$ \gamma - $$ decay

B
$$ \beta - $$ decay

C
Fisslon

D
Fusion

Solution

According to the question, hydrogen is converted into helium and two position and energy. Here, this reaction corresponding fusion.
Question 8
1 / -0

A nucleus $$X$$ initially at rest, undergoes alpha decay according to the equation
$${92}^{{X}^{A}} \rightarrow {Z}^{{Y}^{228}} + \alpha$$
Then, the values of $$A$$ and $$Z$$ are

A
$$94,230$$

B
$$232,90$$

C
$$190,32$$

D
$$230,94$$

Solution

Here, $$\alpha= $$ $$_2He^4$$
Thus, $$_{92}X^A \rightarrow _ZY^{228}+$$ $$_2He^4$$
For balance the equation, $$A=228+4=232$$ and $$92=Z+2$$ or $$Z=90$$
Thus, option B will be the right option.
Question 9
1 / -0

The masses of neutron and proton are 1.0087 and 1.0073 amu respectively. If the neutrons and protons combine to form helium nucleus of mass 4.0015 amu the binding energy of the helium nucleus will be

A
28.4 MeV

B
20.8 MeV

C
27.3 MeV

D
14.2 MeV

Solution

Total protron in helium is 2 and neutron in helium is 2
mass defect $$\Delta M=2(1.0087+1.0073)-4.0015=0.0305 amu$$
Binding energy $$E=931\Delta M=28.4MeV$$
Question 10
1 / -0

An atom of $$_{53}^{131}I$$ and an atom of $$_{53}^{127}I$$ contain the same number of:

A
Quarks

B
Neutrons

C
Nucleons

D
Protons

Solution

Atomic representation of an element is $$^A_ZX$$
where:
$$X:$$ Atomic Symbol
$$Z:$$ Atomic number
$$A:$$ Mass number

Hence, $$^{131}_{53}I$$ and $$^{127}_{53}I$$ has same atomic number but different mass number. Hence, they have same number of protons but different number of neutrons.

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Nuclei Test - 42

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Nuclei Test - 42

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Question 1

$$2^{1/3} : 1$$

$$1 : 3^{1/2}$$

$$3^{1/2} : 1$$

$$1:2^{1/3}$$

Solution

Question 2

Fusion of two nuclei with mass number lying in the range of $$51 < A<100$$ will release energy

Fission of a nucleus lying in the mass range of $$200 < A < 260$$ will release energy when broken into two equal fragments

Both (a) and (b)

None of the above

Solution

Question 3

collision between fast neutrons and nitrogen nuclei present in the atmosphere

action of ultraviolet light from the sun on atmospheric oxygen

action of solar radiations particularly cosmic rays on carbon dioxide present in the atmosphere

lightning discharge in atmosphere

Solution

Question 4

the same number of protons but different number of neutrons

the same number of neutrons but different number of protons

equal number of protons and electrons

equal number of nucleons

Solution

Question 5

Uncontrolled fission reaction

Nuclear fusion reaction

Controlled fission reaction

Photoelectric effect

Solution

Question 6

(iii) and (iv) only

(ii), (iii) and (iv) only

(i), (ii) and (iii) only

(i), (iii) and (iv) only

Solution

Question 7

$$ \gamma - $$ decay

$$ \beta - $$ decay

Fisslon

Fusion

Solution

Question 8

$$94,230$$

$$232,90$$

$$190,32$$

$$230,94$$

Solution

Question 9

28.4 MeV

20.8 MeV

27.3 MeV

14.2 MeV

Solution

Question 10

Quarks

Neutrons

Nucleons

Protons

Solution

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