Answer

Verified

55.2k+ views

**Hint**In the question mass of a single nucleon is given. We can use this to find the total mass of the nucleus. We know the formula for the radius of the nucleus. With the given values we can calculate the mass and volume of the nucleus. From this density can be calculated.

Formula used:

$\rho = \dfrac{m}{V}$ Where $\rho $stands for the density of the nucleus, $m$ stands for the mass of the nucleus, and $V$ stands for the volume of the nucleus.

**Complete Step by step solution**

Let $A$ be the number of nucleons in the nucleus.

Mass of each nucleon is given as, $1.67 \times {10^{ - 27}}kg$

Then the mass of the nucleus can be written as,

$m = A \times 1.67 \times {10^{ - 27}}kg$

The radius of a nucleus can be written as,

$R = {R_0}{A^{\dfrac{1}{3}}}$

It is given that, ${R_0} = 1.4 \times {10^{ - 15}}m$

Since the density of the nucleus can be written as $\rho = \dfrac{m}{V}$ we have to find the volume of the nucleus.

The nucleus is assumed to have a spherical shape. Therefore the volume of the nucleus can be written as,

$V = \dfrac{4}{3}\pi {R^3}$

Substituting $R = {R_0}{A^{\dfrac{1}{3}}}$ in the above equation, we get

$V = \dfrac{4}{3}\pi {\left( {{R_0}{A^{\dfrac{1}{3}}}} \right)^3}$

The volume of the nucleus is thus,

$V = \dfrac{4}{3}\pi R_0^3A$

The mass of the nucleus is,

$m = A \times 1.67 \times {10^{ - 27}}kg$

Now, we can write the density of the nucleus using the above values,

$\rho = \dfrac{m}{V} = \dfrac{{1.67 \times {{10}^{ - 27}}A}}{{\dfrac{4}{3}\pi R_0^3A}}$

$A$ will get cancelled and we substitute the value of ${R_0}$, we get

$\rho = \dfrac{{3 \times 1.67 \times {{10}^{ - 27}}}}{{4 \times 3.14 \times {{\left( {1.4 \times {{10}^{ - 15}}} \right)}^3}}} = 1.453 \times {10^{17}}$

The density of the nucleus will be $1.453 \times {10^{17}}kg/{m^3}$.

The answer is:

**Option (D): $1.453 \times {10^{17}}kg/{m^3}$**

**Note**

The nucleus consists of protons and neutrons, so they are collectively called nucleons. The mass number of an atom is the number of protons and neutrons. The mass of each nucleon is multiplied with the mass number to obtain the total mass of the nucleus.

Recently Updated Pages

Why do we see inverted images in a spoon class 10 physics JEE_Main

A farsighted man who has lost his spectacles reads class 10 physics JEE_Main

State whether true or false The outermost layer of class 10 physics JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

A train starts from rest from a station with acceleration class 11 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main