Nuclei Test

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Nuclei Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

Let $$E_1$$ and $$E_2$$ be the binding energies of two nuclei A and B. It is observed that two nuclei of A combine together to form a B nucleus. This observation is correct only if

A
$$E_1 > E_2$$

B
$$E_2 > E_1$$

C
$$E_2 < 2E_1$$

D
nothing can be said

Solution

$$2A \rightarrow B$$
Possible if B is more stable than A
$$\implies$$ Energy of B is less than two atoms of A
$$ E_2 < 2E_1$$
Question 2
1 / -0

If the Q value of an endothermic reaction is $$11.32 MeV$$, then the minimum energy of the reactant nuclei to carry out the reaction is (in laboratory frame of reference)

A
$$11.32 MeV$$

B
less than $$11.32 MeV$$

C
grater than $$11.32 MeV$$

D
Data is insufficient

Solution

From conservation of energy:
Change in energy $$=$$ Energy of reactants $$-$$ Energy of products $$-$$ $$Q>0$$ (Endothermic)
Therefore, minimum energy of reactants $$>Q=11.32\ MeV$$
Question 3
1 / -0

According to Bohr's Theory of hydrogen atom, the product of the binding energy of the electron in the $$nth$$ orbit and its radius in the $$nth$$ orbit

A
Is proportional to $$n^2$$

B
Is inversely proportional to $$n^3$$

C
Has a constant value of $$10.2\space eV-\mathring{A}$$

D
Has a constant value of $$7.2\space eV-\mathring{A}$$

Solution

From the formulas attached.
The product
$$R(n) \times E(n) = 0.529\cfrac{n^2}{Z} \times 13.6 \cfrac{Z^2}{n^2} eV.-A$$
$$ R(n) \times E(n) = 0.529 \times 13.6 Z eV.-A$$
$$ R(n) \times E(n) = 7.2 eV-A$$
Question 4
1 / -0

Directions For Questions

The sun is an average star of diameter of about $$1.4\times10^{5}$$ and is about $$1.5\times10^{8}$$ km distance away from earth. The average density of the Sun, which consists $$70$$ % $$H$$ and $$28$$ % $$He$$, is about $$1.4$$ times density of water. The pressure and temperatures inside the sun is very large, the temperature being around $$14$$ million $$K$$. At present high temperature thermonuclear reactions take place, converting lighter into heavier ones

...view full instructions

The Sun's mean density is

A
$$1.4\times kg/m^{3}$$

B
$$1.4\times10^{3} kg/m^{3}$$

C
$$1.4\times10^{3} kg/cc $$

D
$$1.4\times kg/cc$$

Solution

Density of water is $$=1000\ kg/m^3$$
Density of sun $$=1.4\times 1000=1.4\times 10^3 ms^{-3}$$
Question 5
1 / -0

An element A decays into an element C by a two-step process:
$$A\rightarrow B+He_2^4$$ and $$B\rightarrow C+{ 2e }_{ -1}^{ 0 }$$.Then

A
A and C are isotopes

B
A and C are isobars

C
B and C are isotopes

D
A and B are isobars

Solution

Conservation of mass no. and charge holds true
$$A \rightarrow B$$
$$Z_B = Z_A -2$$
$$M_B = M_A -4$$
$$B \rightarrow C + 2e$$
$$Z_C = Z_B +2 = Z_A$$
$$M_C = M_B = M_A-4$$
Different mass, but same atomic No.
Therefore, A and C are isotopes.
Question 6
1 / -0

$$_{92}U^{238}$$ absorbs a neutron. The product emits an electron. This product further emits an electron. The result is

A
$$_{94}Pu^{239}$$

B
$$_{90}Pu^{239}$$

C
$$_{93}Pu^{237}$$

D
$$_{94}Pu^{237}$$

Solution

$$_{92}V^{238}+ n \rightarrow _{92}A^{239} $$
$$_{92}A^{239} \rightarrow _{93}B^{239} +e$$
$$_{92}B^{239} \rightarrow _{94}C^{239} +e$$
Finding the element C from periodic table
$$_{94} Pu^{239}$$
Question 7
1 / -0

The minimum frequency of a $$\gamma$$-ray that causes a deuteron to disintegrate into a proton and a neutron is $$(m_d=2.0141 amu, m_p=1.0078 amu, m_n=1.0087 amu.)$$

A
$$2.7\times 10^{20}Hz$$

B
$$5.4\times 10^{20}Hz$$

C
$$10.8\times 10^{20}Hz$$

D
$$21.6\times 10^{20}Hz$$

Solution

$$ D \rightarrow n +p$$
$$\Delta m = m_p +m_n - m_d$$
$$=1.0087 +1.0078 -2.0141 )amu \\ = 2.4 \times 10^{-3} amu$$

Energy required $$=\Delta mc^2$$
$$E/amu = 931\ Mev$$

Energy $$= 931(2.4 \times 10^{-3})= 2.2344\ MeV$$
$$h v = 2.23\ MeV$$
$$v = 5.4 \times 10^{20} Hz$$
Question 8
1 / -0

During a nuclear fusion reaction

A
a heavy nucleus breaks into two fragments by itself

B
a light nucleus bombarded by thermal neutrons breaks up

C
a heavy nucleus bombarded by thermal neutrons breaks up

D
two light nuclei combine to give a heavier nucleus and possibly other products

Solution

A nuclear reaction in which atomic nuclei of low atomic number fuse to form a heavier nucleus with the release of energy is called nuclear fusion.
Question 9
1 / -0

$$^{22}Ne$$ nucleus, after absorbing energy, decays into two $$\alpha$$-particles and an unknown nucleus. The unknown nucleus is

A
nitrogen

B
carbon

C
boron

D
oxygen

Solution

$$^{22}Ne$$ decays
$$\alpha$$ particle = $$ He^{2+}$$
Mass No = 4
$$p=2, n=2$$
So, New mass no. $$= 22 - 8 = 14$$
Atomic No. $$= 10 -4 = 6$$
So, the new element is $$ _6C^{14}$$
Question 10
1 / -0

Binding energy per nucleon for $$C^{12}$$ is 7.68 MeV and for $$C^{13}$$ is $$7.74 MeV$$. The energy required to remove a neutron from $$C^{13}$$ is

A
$$5.49 MeV$$

B
$$8.46 MeV$$

C
$$9.45 MeV$$

D
$$15.49 MeV$$

Solution

$$C^{13} +energy \rightarrow C^{12} +n$$
Energy required to remove one neutron = Difference in total binding energy
$$ = 13 \times 7.74 - 12 \times 7.68 $$ MeV
$$ = 8.46 MeV$$

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Nuclei Test - 32

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Nuclei Test - 32

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Question 1

$$E_1 > E_2$$

$$E_2 > E_1$$

$$E_2 < 2E_1$$

nothing can be said

Solution

Question 2

$$11.32 MeV$$

less than $$11.32 MeV$$

grater than $$11.32 MeV$$

Data is insufficient

Solution

Question 3

Is proportional to $$n^2$$

Is inversely proportional to $$n^3$$

Has a constant value of $$10.2\space eV-\mathring{A}$$

Has a constant value of $$7.2\space eV-\mathring{A}$$

Solution

Question 4

$$1.4\times kg/m^{3}$$

$$1.4\times10^{3} kg/m^{3}$$

$$1.4\times10^{3} kg/cc $$

$$1.4\times kg/cc$$

Solution

Question 5

A and C are isotopes

A and C are isobars

B and C are isotopes

A and B are isobars

Solution

Question 6

$$_{94}Pu^{239}$$

$$_{90}Pu^{239}$$

$$_{93}Pu^{237}$$

$$_{94}Pu^{237}$$

Solution

Question 7

$$2.7\times 10^{20}Hz$$

$$5.4\times 10^{20}Hz$$

$$10.8\times 10^{20}Hz$$

$$21.6\times 10^{20}Hz$$

Solution

Question 8

a heavy nucleus breaks into two fragments by itself

a light nucleus bombarded by thermal neutrons breaks up

a heavy nucleus bombarded by thermal neutrons breaks up

two light nuclei combine to give a heavier nucleus and possibly other products

Solution

Question 9

nitrogen

carbon

boron

oxygen

Solution

Question 10

$$5.49 MeV$$

$$8.46 MeV$$

$$9.45 MeV$$

$$15.49 MeV$$

Solution

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