Nuclei Test

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Nuclei Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

The binding energy per nucleon of $$C^{12}$$ is $$7.68$$ MeV and that of $$C^{13}$$ is $$7.47$$ Mev. The energy required to remove one neutron from $$C^{13}$$ is

A
$$495\ MeV$$

B
$$49.5\ MeV$$

C
$$4.95\ MeV$$

D
$$0.495\ MeV$$

Solution

$$C^{13} \rightarrow C^{12}_1 + ^1n$$

$${BE)_C}^{12} = 12\times 7.68$$$$= 92.16\ MeV$$

$${BE)_C}^{13} = 13\times 7.47$$$$= 97.11\ MeV$$

$$Q = {BE)_C}^{12} - {BE)_C}^{12}$$

$$= 97.11 - 92.16$$

$$={4.95\ MeV}$$
Question 2
1 / -0

The atomic mass of $$_{7}N^{15}$$ is $$15.000108 amu$$ and that of $$_{8}O^{16}$$ is $$15.994915 amu$$. The minimum energy required to remove the least tightly bound proton is (mass of proton is $$1.007825 amu)$$

A
$$0.01 3018 amu$$

B
$$12.13 MeV$$

C
$$13.018 MeV$$

D
$$12.13 eV$$

Solution

$$_8^{16}O \rightarrow ^{15}_7N + ^1_1P$$

$$\Delta m = [15.000108 + 1.007825 - 15.994915]$$
$$= 0.013018 amu$$

$$\Delta E = 0.013018\times 931.478$$ MeV
$$={12.13\ MeV}$$
Question 3
1 / -0

If $$2g$$ of hydrogen is converted into $$1.986 gm$$ Helium in a thermonuclear reaction, the energy released is

A
63 X 10$$^{7}J$$

B
63 X 10$$^{10}J$$

C
126 X 10$$^{10}J$$

D
6.3 X 10$$^{20}J$$

Solution

$$\Delta m = 2 - 1.986$$ $$= {0.014 gm}$$

$$\Delta E = (\dfrac{0.014}{1000}Kg)\times (3\times 10^8)^2$$$$= 126\times 10^{10} J$$
Question 4
1 / -0

$$_{7}N^{14} +_{2}He^{4}\rightarrow $$ X+$$_{1}H^{1}$$ ; X is

A
$$_{9}F^{18}$$

B
$$_{10}Ne^{18}$$

C
$$_{8}O^{17}$$

D
$$_{6}C^{15}$$

Solution

$$_7N^{14} + _2He^4 \rightarrow _Z^A{X} + _1H^1$$

Change balance: $$7 + 2 = Z + 1$$
$$Z = 8$$
Mass balance: $$14 + 4 = A + 1$$
$$A = 17$$
Question 5
1 / -0

Bombardment of lithium with proton gives rise to the following reaction :
$$^{7}_{3}Li+^{1}_{1} H \rightarrow $$2($$^{4}_{2}He) + Q $$
The Q-value is
(atomic masses of lithium, proton and helium are $$7.016$$ amu, $$1.008$$ amu and $$4.004$$ amu respectively)

A
$$14.904$$ MeV

B
$$16.774$$ MeV

C
$$10.634$$ MeV

D
$$18.633$$ MeV

Solution

$$^7_3{Li} + ^1_1H \rightarrow 2 ^4_2{He} + Q$$

Mass defect $$= (7.016 + 1.008 - 2\times 4.004)\mu$$$$= 0.016 amu$$

$$1amu = 931.478 \dfrac{MeV}{C^2}$$

$$E = 0.016\times 931.478 \dfrac{MeV}{C^2}\times C^2$$$$=14.903 MeV$$
Question 6
1 / -0

The masses of neutron and proton are $$1.0087$$ and $$1.0073$$ amu respectively. If the neutrons and protons combine to form a 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

Mass of neutron $$ = 1.0087 amu $$

Mass of proton $$= 1.0073 amu $$

In a helium nucleus,

   protons $$ = 2 $$

   neutrons$$ = 2     $$

Mass(theoritically) $$ = (2\times1.0087 + 2\times1.0073)$$

                               $$ =4.032 $$

Mass defect $$ = (4.032- 4.0015)\ amu $$

$$=0.0305\ amu$$

So, $$1\ amu$$ gives $$931.5\ MeV $$ of energy.

So, $$0.0305\times931.5 MeV $$ of binding energy $$ = 28.4 \ MeV$$
Question 7
1 / -0

A $$\gamma $$ -ray photon creates an electron-positron pair. The rest mass equivalent of electron is 0.5 MeV. KE of the electron - positron system is 0.78 MeV. Then the energy of $$\gamma $$ -ray photon is

A
$$0.28 MeV$$

B
$$1.78 MeV$$

C
$$1.28 MeV$$

D
$$0.14 MeV$$

Solution

The rest mass of electron is $$= 0.5\ MeV$$

As, the momentum is conserved the rest mass of positron should also be $$ 0.5\ MeV$$.

The kinetic energy of the pair is $$0.78\ MeV$$.

$$\therefore$$ The energy of $$\gamma$$ ray photon is $$= (0.5+0.5+0.78) \ MeV= 1.78 \ MeV$$
Question 8
1 / -0

Assertion (A) : All the radioactive elements are ultimately converted into lead
Reason (R): All the elements above lead are unstable

A
Both A and R are true and R is correct explanation of A

B
Both A and R are true and R is not correct explanation of A

C
A is true but R is false

D
A is false but R is true

Solution

For all $$4n, 4n+2$$ series elements, on emission of different kind of rays, they form different isotopes of lead and also all element above lead are unstable .
But, $$4n+1$$ series elements (Neptunium series), end in $$^{209}_{83}Bi $$ (Bismuth not lead)
Question 9
1 / -0

Assertion (A): Binding energy per nucleon is the measure of the stability of the nucleus.
Reason (R): Binding energy per nucleon is more for heavier nuclides.

A
Both A and R are true and R is correct explanation of A.

B
Both A and R are true and R is not the correct explanation of A.

C
A is true but R is false

D
A is false but R is true

Solution

The binding energy is the energy that is released when a nucleus is assembled from its constituent nucleons Hence, the energy equivalent of the mass-defect is called the binding-energy of the nucleus.
The heavier the nucleus, the greater the internal repulsive forces due to the greater number of protons and less energy must be applied to remove a nucleon from the nucleus, hence the binding energy is lower. Thus for lighter nuclei binding energy is more. The greater the binding energy, the more stable the nucleus is.
Question 10
1 / -0

In the nuclear fusion reaction : $$^{2}_{1}H+ ^{3}_{1}H \rightarrow $$ $$^{4}_{2}He+n $$ , given that the repulsive potential energy between the two nuclei is $$\sim 7.7 \times 10^{-14}$$J, the temperature to which the gases must be heated to initiate the reaction is nearly
(Boltzmann's constant $$k=$$1.38 x 10$$^{-23}$$J)

A
$$10^{7} K$$

B
$$10^{5} K$$

C
$$10^{3} K$$

D
$$10^{9}K$$

Solution

The repulsive potential energy $$=\dfrac{3}{2}kT$$

$$7.7\times 10^{-14}=\dfrac{3}{2}\times 1.38\times\times 10^{-23} \times T$$

$$\rightarrow \ T = 3.7\times 10^9 K \sim 10^9 K$$

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Nuclei Test - 25

Result

Nuclei Test - 25

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SHARING IS CARING

Question 1

$$495\ MeV$$

$$49.5\ MeV$$

$$4.95\ MeV$$

$$0.495\ MeV$$

Solution

Question 2

$$0.01 3018 amu$$

$$12.13 MeV$$

$$13.018 MeV$$

$$12.13 eV$$

Solution

Question 3

63 X 10$$^{7}J$$

63 X 10$$^{10}J$$

126 X 10$$^{10}J$$

6.3 X 10$$^{20}J$$

Solution

Question 4

$$_{9}F^{18}$$

$$_{10}Ne^{18}$$

$$_{8}O^{17}$$

$$_{6}C^{15}$$

Solution

Question 5

$$14.904$$ MeV

$$16.774$$ MeV

$$10.634$$ MeV

$$18.633$$ MeV

Solution

Question 6

$$28.4 MeV$$

$$20.8 MeV$$

$$27.3 MeV$$

$$14.2 MeV$$

Solution

Question 7

$$0.28 MeV$$

$$1.78 MeV$$

$$1.28 MeV$$

$$0.14 MeV$$

Solution

Question 8

Both A and R are true and R is correct explanation of A

Both A and R are true and R is not correct explanation of A

A is true but R is false

A is false but R is true

Solution

Question 9

Both A and R are true and R is correct explanation of A.

Both A and R are true and R is not the correct explanation of A.

A is true but R is false

A is false but R is true

Solution

Question 10

$$10^{7} K$$

$$10^{5} K$$

$$10^{3} K$$

$$10^{9}K$$

Solution

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