What is Density

**Density** is defined as the **mass per unit volume**. It is an **intensive property**, which is mathematically defined as mass divided by volume:

**ρ = m/V**

In words, the density (ρ) of a substance is the total mass (m) of that substance divided by the total volume (V) occupied by that substance. The standard SI unit is **kilograms per cubic meter** (**kg/m ^{3}**). The Standard English unit is

**pounds mass per cubic foot**(

**lbm/ft**). The density (ρ) of a substance is the reciprocal of its

^{3}**specific volume**(ν).

**ρ = m/V = 1/ρ**

**Specific volume** is an** intensive variable**, whereas volume is an extensive variable. The standard unit for specific volume in the SI system is cubic meters per kilogram (m^{3}/kg). The standard unit in the English system is cubic feet per pound mass (ft^{3}/lbm). Changes of Density

Coolant acceleration in a reactor core

## Densest Materials on the Earth

Since **nucleons** (**protons** and **neutrons**) make up most of the mass of ordinary atoms, the density of normal matter tends to be limited by how closely we can pack these nucleons and depends on the internal atomic structure of a substance. The **densest material** found on earth is the **metal osmium**, but its density pales by comparison to the densities of exotic astronomical objects such as white** dwarf stars** and **neutron stars**.

**List of densest materials:**

- Osmium – 22.6 x 10
^{3}kg/m^{3} - Iridium – 22.4 x 10
^{3}kg/m^{3} - Platinum – 21.5 x 10
^{3}kg/m^{3} - Rhenium – 21.0 x 10
^{3}kg/m^{3} - Plutonium – 19.8 x 10
^{3}kg/m^{3} - Gold – 19.3 x 10
^{3}kg/m^{3} - Tungsten – 19.3 x 10
^{3}kg/m^{3} - Uranium – 18.8 x 10
^{3}kg/m^{3} - Tantalum – 16.6 x 10
^{3}kg/m^{3} - Mercury – 13.6 x 10
^{3}kg/m^{3} - Rhodium – 12.4 x 10
^{3}kg/m^{3} - Thorium – 11.7 x 10
^{3}kg/m^{3} - Lead – 11.3 x 10
^{3}kg/m^{3} - Silver – 10.5 x 10
^{3}kg/m^{3}

It must be noted, plutonium is a man-made isotope and is created from uranium in nuclear reactors. But, In fact, scientists have found trace amounts of naturally-occurring plutonium.

If we include man made elements, the densest so far is** Hassium**. **Hassium** is a chemical element with symbol **Hs** and atomic number 108. It is a synthetic element (first synthesised at Hasse in Germany) and radioactive. The most stable known isotope, ** ^{269}Hs**, has a half-life of approximately 9.7 seconds. It has an estimated density of

**40.7 x 10**. The density of Hassium results from its

^{3}kg/m^{3}**high atomic weight**and from the significant decrease in

**ionic radii**of the elements in the lanthanide series, known as

**lanthanide and actinide contraction**.

The density of Hassium is followed by **Meitnerium** (element 109, named after the physicist Lise Meitner), which has an estimated density of** 37.4 x 10 ^{3} kg/m^{3}**.

Density – Important property in gamma rays shielding

## Density of various Materials – Examples

Density of Water – Specific Volume

**Density of Heavy WaterDensity of Steam**

Density of Steel Density of Zirconium Density of Uranium

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## Density of Nuclear Matter

**Nuclear density** is the density of the nucleus of an atom. It is the ratio of mass per unit volume inside the nucleus. Since atomic nucleus carries most of atom’s mass and atomic nucleus is very small in comparison to entire atom, the nuclear density is very high.

The nuclear density for a typical nucleus can be approximately calculated from the size of the nucleus and from its mass. **Typical nuclear radii** are of the order **10 ^{−14} m**. Assuming spherical shape, nuclear radii can be calculated according to following formula:

r = r_{0} . A^{1/3}

where r_{0} = 1.2 x 10^{-15 }m = 1.2 fm

For example, **natural uranium** consists primarily of isotope ^{238}U (99.28%), therefore the atomic mass of uranium element is close to the atomic mass of ^{238}U isotope (238.03u). Its radius of this nucleus will be:

r = r_{0} . A^{1/3} = 7.44 fm.

Assuming it is spherical, its volume will be:

V = 4πr^{3}/3 = 1.73 x 10^{-42} m^{3}.

The usual definition of nuclear density gives for its density:

ρ_{nucleus} = m / V = 238 x 1.66 x 10^{-27} / (1.73 x 10^{-42}) = **2.3 x 10 ^{17} kg/m^{3}**.

Thus, the density of nuclear material is more than 2.10^{14} times greater than that of water. It is an immense density. The descriptive term *nuclear density* is also applied to situations where similarly high densities occur, such as within neutron stars. Such immense densities are also found in neutron stars.

## Exercise:

*40m^3 of liquid is mixed with 60m^3 of another liquid Q. If the density of P and Q are 1.00kg m^-3 and 1.6kg m^-3 respectively.*

What is the density of the mixture

A. 0.05kg m^-3

B. 1.25kg m^-3

C. 1.30kg m^-3

D. 1.36kg m^-3

Solutions to the above question:

D=mass/volume.

For P

1=m/40

M=40

For q

1.6=m/60

M=96

For the mixture.

Total Volume =100

Total mass =136

i.e to say

Density of the mixture=total Mass/total Volume .

Density of the Mixture=136/100=1.36

There for the option D is the answer to the above question.

Which is D of the mixture=1.36kg/m^-3///

Another Formula to solve this Density is:

D=m/v

1×40=m1

M1=40

1.6×60=96

D=(m1 + m2)/v

D=96+40/100

We still arrive at 1.36kg/m³.