Nuclei Test

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Nuclei Test - 41

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Weekly Quiz Competition

Question 1
1 / -0

How many grams are there in a $$7.0$$ mole sample of sodium hydroxide?

A
$$40.0g$$

B
$$140.0\ g$$

C
$$280.0\ g$$

D
$$340.0\ g$$

E
$$420.0\ g$$

Solution

The formula of sodium hydroxide is $$NaOH$$
Atomic weight of $$Na$$ = $$23\ {g}/{mol}$$
Atomic weight of $$ O $$ = $$16\ {g}/{mol}$$
Atomic weight of $$H$$ = $$ 1\ {g}/{mol}$$
$$\therefore $$ molecular weight of $$NaOH$$ = atomic mass of $$Na$$ + atomic mass of $$O$$ + atomic mass of $$H$$
= $$23 + 16 + 1 = 40\ {g}/{mol}$$
Therefore, 1 mole of $$NaOH = 40\ g/mol$$
7 moles of $$ NaOH = 7 \ mole \times 40\ g/mol= 280g$$

Hence, option $$B$$ is correct.
Question 2
1 / -0

The mass defect in a nucleus is $$3.5$$ amu. Then the binding energy of the nucleus is.

A
$$3258.5$$ MeV

B
$$325.85$$ MeV

C
$$32.58$$ MeV

D
$$3.258$$ MeV

Solution

A
Binding energy =(mass defect) $$c^{2} = (\Delta m) c^{2}$$
$$=\Delta(931)MeV$$
$$=3.5×931 = 3258.5 MeV$$
Question 3
1 / -0

Calculate the mass defect.

A
$$2.014$$u

B
$$1.0087$$u

C
$$0.01876$$u

D
$$0.0234$$u

Solution

Possible fusion reaction
$$_{ 1 }^{ 2 }{ H }+_{ 1 }^{ 3 }{ H }\rightarrow _{ x }^{ y }{ He }+_{ 0 }^{ 1 }{ n }\\ 1+1=x+0\Rightarrow x=2\\ 2+3=y+1\Rightarrow y=4\\ _{ 1 }^{ 2 }{ H }+_{ 1 }^{ 3 }{ H }\rightarrow _{ 2 }^{ 4 }{ He }+_{ 0 }^{ 1 }{ n }$$
Mass defect $$=\triangle m=\left( m\left( _{ 1 }^{ 2 }{ H } \right) +m\left( _{ 1 }^{ 3 }{ H } \right) \right) -\left( m\left( _{ 2 }^{ 4 }{ He } \right) +m\left( _{ 0 }^{ 1 }{ n } \right) \right) \\ =(2.014012+3.016050-4.002603-1.0087)u\\ =0.018759u\approx 0.01876u$$
Question 4
1 / -0

The Q value is the ________ energy released in the decay at rest.

A
kinetic

B
potential

C
thermal

D
optical

Solution

The Q value is the amount of energy released by a nuclear reaction. It is based on the mass-energy equivalence.
The Q value is defined as change in kinetic energy, i.e $$Q=KE_{final}-KE_{initial}=(m_{final}-m_{initial})c^2$$.
Question 5
1 / -0

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

A
$$26.9$$MeV

B
$$25.8$$MeV

C
$$23.6$$MeV

D
$$12.9$$MeV

Solution

The nuclear reaction is: $$_1H^2 + _1H^2 \rightarrow _2He^4$$
Binding energy of deutron, $$E_d = 1.1\times 2 = 2.2$$ MeV
Binding energy of helium, $$E_{He} = 7\times 4 = 28$$ MeV
Energy released, $$Q = E_{He} - 2E_d$$
$$\therefore$$ $$Q = 28 - 2(2.2) = 23.6$$ MeV
Question 6
1 / -0

Which of the following is a nuclear reaction?

A
Two hydrogen atoms combine to form hydrogen molecule

B
Sodium atom gives up an electron to become sodium ion

C
Water splits up into hydrogen and oxygen by electrolysis

D
Isotopes of Hydrogen nuclei combine to form helium nuclei

Solution

Isotopes of hydrogen nuclei combine to form helium nuclei
$$_{1}H^{3}+_{1}H^{2}\rightarrow_{2}He^{4}+n^{1}$$+ energy
Question 7
1 / -0

An alpha particle ($$^4He$$)has a mass of 4.00300 amu. A proton has mass of 1.00783 amu and a neutron has mass of 1.00867 amu respectively. The binding energy of alpha particle estimated from these data is the closest to

A
27.9 MeV

B
22.3 MeV

C
35.0 MeV

D
20.4 MeV

Solution

An alpha particle $$(_2^4He)$$ has 2 protons and two neutrons.
Mass defect $$\Delta M = 2m_p + 2m_n - m_{He}$$
$$\therefore$$ $$\Delta M=2(1.00783) + 2(1.00867)-4.00300$$ $$ = 0.03000$$ amu
Binding energy of alpha particle B.E$$ = \Delta M c^2$$
$$\therefore$$ B.E $$ = 0.03000 \times 931.5 =27.9$$ MeV $$(\because 1$$ amu $$c^2=931.5 MeV$$ $$)$$
Question 8
1 / -0

The equation $$E=mc^2$$ was theoretical. It received experimental proof from.

A
Nuclear reactions carried out in the laboratory

B
Measurement of molecular mass of a compound formed by chemical comination

C
Measurement of molecular mass of products of decomposition

D
The phenomenon of radioactivity

Solution

The phenomenon of radioactivity
The equation $$E=m{c}^{2}$$ was found therotically and it is not proved initially. Later in the theorem received the proof from the phenomenon of radioactivity.
Question 9
1 / -0

$$4_1H^1\rightarrow \ _2He^4+2e^0_{+1}+26$$ MeV represents

A
Fusion

B
Fission

C
$$\beta$$-decay

D
$$\gamma$$decay

Solution
Question 10
1 / -0

When a radioactive isotope $$_{88} Ra^{228}$$ decays in series by the emission of three $$\alpha $$-particles and a $$\beta$$ particle the isotope finally formed is :

A
$$_{84} X^{220}$$

B
$$_{86}X^{222}$$

C
$$_{83}X^{216}$$

D
$$_{83}X^{215}$$

Solution

In each alpha decay, mass number of the parent nucleus decreases by $$4$$ units while atomic number decreases by $$2$$ units. In each beta decay, atomic number increases by $$1$$ unit but mass number remains the same.
So, mass number of the isotope formed $$A = 228-3\times 4 = 216$$
Atomic number $$Z = 88-3\times 2+1 = 83$$
So correct answer is option C.

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Nuclei Test - 41

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Nuclei Test - 41

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Question 1

$$40.0g$$

$$140.0\ g$$

$$280.0\ g$$

$$340.0\ g$$

$$420.0\ g$$

Solution

Question 2

$$3258.5$$ MeV

$$325.85$$ MeV

$$32.58$$ MeV

$$3.258$$ MeV

Solution

Question 3

$$2.014$$u

$$1.0087$$u

$$0.01876$$u

$$0.0234$$u

Solution

Question 4

kinetic

potential

thermal

optical

Solution

Question 5

$$26.9$$MeV

$$25.8$$MeV

$$23.6$$MeV

$$12.9$$MeV

Solution

Question 6

Two hydrogen atoms combine to form hydrogen molecule

Sodium atom gives up an electron to become sodium ion

Water splits up into hydrogen and oxygen by electrolysis

Isotopes of Hydrogen nuclei combine to form helium nuclei

Solution

Question 7

27.9 MeV

22.3 MeV

35.0 MeV

20.4 MeV

Solution

Question 8

Nuclear reactions carried out in the laboratory

Measurement of molecular mass of a compound formed by chemical comination

Measurement of molecular mass of products of decomposition

The phenomenon of radioactivity

Solution

Question 9

Fusion

Fission

$$\beta$$-decay

$$\gamma$$decay

Solution

Question 10

$$_{84} X^{220}$$

$$_{86}X^{222}$$

$$_{83}X^{216}$$

$$_{83}X^{215}$$

Solution

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