Unit 5 section 1 Nuclear Radius and Density

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The Size of the Atom

Using scattering and diffraction methods, we know that the radius of an atom is 0.05nm or 5x10^-11m and the radius of the smallest nucleus is 1fm or 1x10^-15

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Nucleons

Particles that make up the nucleus are protons and neutrons alternatively called nucleons. The number of nucleons in an atom is the nucleons/mass number. The more nucleons added to the nucleus the bigger it gets.

A graph to show how nuclear radius increases with increasing nucleon number will be a line curving upwards and to the right.

A graph to show how nuclear radius is directly proportional to the cube root of the nucleon number will be a straight line through the origin.

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Calculating the Radius of a Nucleus

r=r0xA^1/3

r: radius, m

ro: constant: 1.4x10^-15m

A: nucleon number

1/3 is also the same as the cube root

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Calculating Nuclear Density

All nucleons take up about e same volume in a nucleus. Because they all have nearly the same mass which also means they all have a similar density, p.

Density example when given the mass:

Carbon:

1. Radius=r=roxA^1/3

2. Volume=V=4/3xPixr^3

3. Density=p=m/v

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Understanding Nuclear Density

Nuclear density is significantly larger than atomic density - this suggest three important facts about the structure of an atom:

-most of the atoms mass is in its nucleus

-the nucleus is mall compared to the atom

-an atom must contain a lot of empty space

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