What is the approximate radius R of 208 82Pb? Express your answer in meters to two significant figures. R = 7.10*10-15 m

Assuming that each nucleus is roughly spherical and that its
mass is roughly equal to *A* (in atomic mass units u), what
is the density *?* of a nucleus with nucleon number
*A*?

Express your answer in terms of *A*, *R*0, and
*?*.

## Answer

## General guidance

Initially, the approximate nucleus radius can be calculated by using the relation between the radius, absolute radius and the nucleon number.

Finally, the density of the nucleus can be calculated by using the relation between mass, volume and density.

The expression for the radius of the nucleus is,

Here, is the radius, is the absolute radius, and is the mass number.

The expression for the density of the nucleus is,

Here, is the density of the nucleus, *M* is the mass of the sphere, and *V* is the volume.

The volume of the sphere is,

## Step-by-step

### Step 1 of 2

**(a)**

The expression for the radius is,

The atomic mass number for lead (Pb) is, .

The absolute radius of the nuclei is,

Substitute for and for .

**The radius of the nucleus is****.**

The radius of the nucleus is directly proportional to the absolute radius and the mass number.

Protons and neutrons are bound together to form a nucleus. The diameter of the nucleus is in the range of 1.75fm.

### Step 2 of 2

**(b)**

The expression for the density is,

…… (1)

The volume of the sphere is,

The expression for the radius of the nucleus is,

Replace for *V* and for in the equation (1).

**The expression for density of the nucleus is****.**

The density of the nucleus is the ratio of mass number to the volume of the nucleus.

The average nuclear density of the nucleus of an atom is .

### Answer

**The radius of the nucleus is****.**

**The expression for density of the nucleus is****.**

### Answer only

**The radius of the nucleus is****.**

**The expression for density of the nucleus is****.**

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