Nuclei Test

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Nuclei Test - 53

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Weekly Quiz Competition

Question 1
1 / -0

Binding energy of deuterium is $$2.23\ MeV$$, then its mass defect in a.m.u. is

A
$$-0.0024$$

B
$$-0.0012$$

C
$$0.0012$$

D
$$0.0024$$

Solution

Mass defect $$\Delta m=\dfrac {2.23}{931}=0.0024 amu$$.
Question 2
1 / -0

A heavy nucleus $$X$$ of mass number $$240$$ and binding energy per nucleon $$7.6MeV$$ is split into two fragments $$Y$$ and $$Z$$ of mass numbers $$110$$ and $$130$$ the binding energy of nucleons in $$Y$$ is $$8.5MeV$$ per nucleon$$.$$ Calculate the energy $$Q$$ released per fission in $$MeV.$$

A
240$$\mathrm { Mev }$$

B
216$$\mathrm { Mev }$$

C
120$$\mathrm { Mev }$$

D
108$$\mathrm { Mev }$$

Solution

The nuclear reaction is
$${X^{240}} \to {Y^{110}} + {Z^{130}} + Q$$
As per given data
$$Q = 110 \times 8.5 + 130 \times 8.5 - 240 \times 7.6$$
$$ = 240\left( {0.9} \right)MeV = 216MeV$$
Hence,
option $$(B)$$ is correct answer.
Question 3
1 / -0

A nuclear reactor delivers power of 10W, find fuel consumed by the reactor per hour if its efficiency is $$20\%$$, Given $$c=3 \times 10^8 m/s$$

A
$$2 \times 10^{-6}g/hr$$

B
$$9 \times 10^{-12}g/hr$$

C
$$8 \times 10^{-9}g/hr$$

D
$$2 \times 10^{-9}g/hr$$

Solution

As fuel consumed by the react or with efficiency 20%. Then energy will be:
$$E = \dfrac{100 \times 100}{20} = 50 \ J/s$$
As $$E= mc^2, m= \dfrac{E}{c^2}$$
$$m= \dfrac{50}{ ( 3 \times 10^8)^2} kg/s = \dfrac{50 \times 3600 \times 10^3}{( 3 \times 10^8)^2} g / hr= 2 \times 10^{-9} g / hr$$
Question 4
1 / -0

In $$\overset { 14 }{ \underset { 7 }{ N } } $$ if mass attributed to electron were doubled & the mass attributed to protons were halved, the atomic mass would become approximately:-

A
Halved

B
Doubled

C
Reduced by 25%

D
Remain same

Solution
Question 5
1 / -0

48 g of Mg contain the same number of atoms as 160 g another mono-atomic element.The atomic mass the element is:

A
24

B
320

C
80

D
40

Solution
Question 6
1 / -0

Atomic mass of $$_{ 6 }^{ 13 }{ C }$$ is $$13.00335$$ amu and its mass number is $$13.0$$. If amu $$=931$$MeV, binding energy of the neutrons present in the nucleus is

A
3.10$$\mathrm { MeV }$$

B
974$$\mathrm { MeV }$$

C
97.4$$\mathrm { MeV }$$

D
9.974$$\mathrm { MeV }$$

Solution

Binding energy is the product of mass deflect and $$c$$ square$$.$$
Now$$,$$ $$13.00335 - 13 = 0.00335\,u.$$
$$ \Rightarrow B.E = 931 \times 0.00335 = 3.10\,MeV$$
Hence,
option $$(A)$$ is correct answer.
Question 7
1 / -0

Among $$\alpha$$ -decay and $$\beta$$ -decay which cause a change of element?

A
Both $$\alpha$$ -decay and $$\beta$$ -decay

B
Only $$\alpha$$ -decay

C
Only $$\beta$$ -decay

D
None of them.
Question 8
1 / -0

Nucleus A is converted into C through the following reactions,
A$$\rightarrow $$B+$$\alpha $$
B$$\rightarrow$$C+2$$\beta $$
then,

A
A and B are isotopes

B
A and C are isobars

C
A and B are isobars

D
A and C are isotopes
Question 9
1 / -0

The nucleus of mass $$M + \Delta m$$ is at rest and decays into two daughter nuclei of equal mass $$\dfrac { M } { 2 }$$ each. Speed of light is $$ c.$$ This binding energy per nucleon for the parent nucleus is $$E _ { 1 }$$ and that for the daughter nuclei is $$E _ { 2 }.$$ Then :

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

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

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

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

Solution
Question 10
1 / -0

A sample containing same number of two nuclei A and B start decaying. The decay constant of A and B are $$10 \lambda$$ and $$\lambda$$. The time after which $$\dfrac{N_A}{N_B}$$ becomes $$\dfrac{1}{e}$$ is

A
$$\dfrac{1}{9 \lambda}$$

B
$$\dfrac{1}{18 \lambda}$$

C
$$\dfrac{2}{9 \lambda}$$

D
$$\dfrac{3}{19 \lambda}$$

Solution

$$\dfrac{N_A}{N_B} = \dfrac{N_0 e^{-10 \lambda t}}{N_0 e^{-\lambda t}} = \dfrac{1}{e}$$
$$\Rightarrow e^{-9 \lambda t} = e^{-1}$$
$$\Rightarrow 9 \lambda t = 1$$
$$\Rightarrow t = \dfrac{1}{9 \lambda}$$

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Re-Attempt Weekly Quiz Competition

Nuclei Test - 53

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Nuclei Test - 53

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SHARING IS CARING

Question 1

$$-0.0024$$

$$-0.0012$$

$$0.0012$$

$$0.0024$$

Solution

Question 2

240$$\mathrm { Mev }$$

216$$\mathrm { Mev }$$

120$$\mathrm { Mev }$$

108$$\mathrm { Mev }$$

Solution

Question 3

$$2 \times 10^{-6}g/hr$$

$$9 \times 10^{-12}g/hr$$

$$8 \times 10^{-9}g/hr$$

$$2 \times 10^{-9}g/hr$$

Solution

Question 4

Halved

Doubled

Reduced by 25%

Remain same

Solution

Question 5

24

320

80

40

Solution

Question 6

3.10$$\mathrm { MeV }$$

974$$\mathrm { MeV }$$

97.4$$\mathrm { MeV }$$

9.974$$\mathrm { MeV }$$

Solution

Question 7

Both $$\alpha$$ -decay and $$\beta$$ -decay

Only $$\alpha$$ -decay

Only $$\beta$$ -decay

None of them.

Question 8

A and B are isotopes

A and C are isobars

A and B are isobars

A and C are isotopes

Question 9

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

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

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

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

Solution

Question 10

$$\dfrac{1}{9 \lambda}$$

$$\dfrac{1}{18 \lambda}$$

$$\dfrac{2}{9 \lambda}$$

$$\dfrac{3}{19 \lambda}$$

Solution

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