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PHXII13:NUCLEI

363857 Assume that the nuclear mass is of the order of $10^{- 27} k g$ and the nuclear radius is of the order of $10^{- 15} m$ . The nuclear density is of the order of

1

10^{2} k g / m^{3}

2

10^{10} k g / m^{3}

3

10^{17} k g / m^{3}

4

10^{31} k g / m^{3}

Explanation:

Density $d = \frac{M}{V} = \frac{M}{\frac{4}{3} π R^{3}}$
$d = \frac{3 M}{4 π R^{3}} = \frac{3}{4 π} (\frac{A m}{A R_{0}^{3}}) = \frac{3 m}{4 π R_{0}^{3}}$
$= \frac{3}{4 π} \frac{10^{- 27}}{10^{- 45}}$
$\Rightarrow d$ is of the order of $10^{17} k g / m^{3}$ .
Correct option is (3).

PHXII13:NUCLEI

363858 The volume occupied by an atom is greater than the volume of the nucleus by a factor of about

1

10^{10}

2

10^{15}

3

10^{1}

4

10^{5}

Explanation:

Radius of atom $\approx 10^{- 10} m$
Radius of nucleus $\approx 10^{- 15} m$
$\frac{V o l u m e o f a t o m}{V o l u m e o f n u c l e u s} = \frac{\frac{4}{3} π r_{1}^{3}}{\frac{4}{3} π r_{2}^{3}} = {(\frac{10^{- 10}}{10^{- 15}})}^{3} = 10^{15}$

PHXII13:NUCLEI

363859 Assertion :
Density of all the nuclei is same.
Reason :
Radius of nucleus is directly proportional to the cube root of mass number.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

Through experimental observation, it has been determined that the average radius of a nucleus is described by the equation
$R = R_{0} A^{1 / 3}, R_{0} = 1.5 \times 10^{- 15} m$
Density $ρ = \frac{A m_{p}}{(\frac{4}{3} π R^{3}) A} = 2.32 \times 10^{17} k g / m^{3}$
which is constant for all $A$ . So correct option is (1).

PHXII13:NUCLEI

363860 Assertion :
All nuclei are not of same size.
Reason :
Size depends on atomic mass.

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The radius of nucleus is given by $R = R_{0} A^{1 / 3},$ where $R_{0}$ is a constant $= 1.1 \times 10^{- 15} m .$ For different nuclei mass number $A$ is different, therefore $R$ is different. So option (1) is correct.

PHXII13:NUCLEI

363857 Assume that the nuclear mass is of the order of $10^{- 27} k g$ and the nuclear radius is of the order of $10^{- 15} m$ . The nuclear density is of the order of

1

10^{2} k g / m^{3}

2

10^{10} k g / m^{3}

3

10^{17} k g / m^{3}

4

10^{31} k g / m^{3}

Explanation:

Density $d = \frac{M}{V} = \frac{M}{\frac{4}{3} π R^{3}}$
$d = \frac{3 M}{4 π R^{3}} = \frac{3}{4 π} (\frac{A m}{A R_{0}^{3}}) = \frac{3 m}{4 π R_{0}^{3}}$
$= \frac{3}{4 π} \frac{10^{- 27}}{10^{- 45}}$
$\Rightarrow d$ is of the order of $10^{17} k g / m^{3}$ .
Correct option is (3).

PHXII13:NUCLEI

363858 The volume occupied by an atom is greater than the volume of the nucleus by a factor of about

1

10^{10}

2

10^{15}

3

10^{1}

4

10^{5}

Explanation:

Radius of atom $\approx 10^{- 10} m$
Radius of nucleus $\approx 10^{- 15} m$
$\frac{V o l u m e o f a t o m}{V o l u m e o f n u c l e u s} = \frac{\frac{4}{3} π r_{1}^{3}}{\frac{4}{3} π r_{2}^{3}} = {(\frac{10^{- 10}}{10^{- 15}})}^{3} = 10^{15}$

PHXII13:NUCLEI

363859 Assertion :
Density of all the nuclei is same.
Reason :
Radius of nucleus is directly proportional to the cube root of mass number.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

Through experimental observation, it has been determined that the average radius of a nucleus is described by the equation
$R = R_{0} A^{1 / 3}, R_{0} = 1.5 \times 10^{- 15} m$
Density $ρ = \frac{A m_{p}}{(\frac{4}{3} π R^{3}) A} = 2.32 \times 10^{17} k g / m^{3}$
which is constant for all $A$ . So correct option is (1).

PHXII13:NUCLEI

363860 Assertion :
All nuclei are not of same size.
Reason :
Size depends on atomic mass.

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The radius of nucleus is given by $R = R_{0} A^{1 / 3},$ where $R_{0}$ is a constant $= 1.1 \times 10^{- 15} m .$ For different nuclei mass number $A$ is different, therefore $R$ is different. So option (1) is correct.

PHXII13:NUCLEI

363857 Assume that the nuclear mass is of the order of $10^{- 27} k g$ and the nuclear radius is of the order of $10^{- 15} m$ . The nuclear density is of the order of

1

10^{2} k g / m^{3}

2

10^{10} k g / m^{3}

3

10^{17} k g / m^{3}

4

10^{31} k g / m^{3}

Explanation:

Density $d = \frac{M}{V} = \frac{M}{\frac{4}{3} π R^{3}}$
$d = \frac{3 M}{4 π R^{3}} = \frac{3}{4 π} (\frac{A m}{A R_{0}^{3}}) = \frac{3 m}{4 π R_{0}^{3}}$
$= \frac{3}{4 π} \frac{10^{- 27}}{10^{- 45}}$
$\Rightarrow d$ is of the order of $10^{17} k g / m^{3}$ .
Correct option is (3).

PHXII13:NUCLEI

363858 The volume occupied by an atom is greater than the volume of the nucleus by a factor of about

1

10^{10}

2

10^{15}

3

10^{1}

4

10^{5}

Explanation:

Radius of atom $\approx 10^{- 10} m$
Radius of nucleus $\approx 10^{- 15} m$
$\frac{V o l u m e o f a t o m}{V o l u m e o f n u c l e u s} = \frac{\frac{4}{3} π r_{1}^{3}}{\frac{4}{3} π r_{2}^{3}} = {(\frac{10^{- 10}}{10^{- 15}})}^{3} = 10^{15}$

PHXII13:NUCLEI

363859 Assertion :
Density of all the nuclei is same.
Reason :
Radius of nucleus is directly proportional to the cube root of mass number.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

Through experimental observation, it has been determined that the average radius of a nucleus is described by the equation
$R = R_{0} A^{1 / 3}, R_{0} = 1.5 \times 10^{- 15} m$
Density $ρ = \frac{A m_{p}}{(\frac{4}{3} π R^{3}) A} = 2.32 \times 10^{17} k g / m^{3}$
which is constant for all $A$ . So correct option is (1).

PHXII13:NUCLEI

363860 Assertion :
All nuclei are not of same size.
Reason :
Size depends on atomic mass.

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The radius of nucleus is given by $R = R_{0} A^{1 / 3},$ where $R_{0}$ is a constant $= 1.1 \times 10^{- 15} m .$ For different nuclei mass number $A$ is different, therefore $R$ is different. So option (1) is correct.

PHXII13:NUCLEI

363857 Assume that the nuclear mass is of the order of $10^{- 27} k g$ and the nuclear radius is of the order of $10^{- 15} m$ . The nuclear density is of the order of

1

10^{2} k g / m^{3}

2

10^{10} k g / m^{3}

3

10^{17} k g / m^{3}

4

10^{31} k g / m^{3}

Explanation:

Density $d = \frac{M}{V} = \frac{M}{\frac{4}{3} π R^{3}}$
$d = \frac{3 M}{4 π R^{3}} = \frac{3}{4 π} (\frac{A m}{A R_{0}^{3}}) = \frac{3 m}{4 π R_{0}^{3}}$
$= \frac{3}{4 π} \frac{10^{- 27}}{10^{- 45}}$
$\Rightarrow d$ is of the order of $10^{17} k g / m^{3}$ .
Correct option is (3).

PHXII13:NUCLEI

363858 The volume occupied by an atom is greater than the volume of the nucleus by a factor of about

1

10^{10}

2

10^{15}

3

10^{1}

4

10^{5}

Explanation:

Radius of atom $\approx 10^{- 10} m$
Radius of nucleus $\approx 10^{- 15} m$
$\frac{V o l u m e o f a t o m}{V o l u m e o f n u c l e u s} = \frac{\frac{4}{3} π r_{1}^{3}}{\frac{4}{3} π r_{2}^{3}} = {(\frac{10^{- 10}}{10^{- 15}})}^{3} = 10^{15}$

PHXII13:NUCLEI

363859 Assertion :
Density of all the nuclei is same.
Reason :
Radius of nucleus is directly proportional to the cube root of mass number.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

Through experimental observation, it has been determined that the average radius of a nucleus is described by the equation
$R = R_{0} A^{1 / 3}, R_{0} = 1.5 \times 10^{- 15} m$
Density $ρ = \frac{A m_{p}}{(\frac{4}{3} π R^{3}) A} = 2.32 \times 10^{17} k g / m^{3}$
which is constant for all $A$ . So correct option is (1).

PHXII13:NUCLEI

363860 Assertion :
All nuclei are not of same size.
Reason :
Size depends on atomic mass.

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The radius of nucleus is given by $R = R_{0} A^{1 / 3},$ where $R_{0}$ is a constant $= 1.1 \times 10^{- 15} m .$ For different nuclei mass number $A$ is different, therefore $R$ is different. So option (1) is correct.

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