10.1 Properties of nuclei  (Page 2/14)

Why do neutrons outnumber protons in heavier nuclei ( [link] )? The answer to this question requires an understanding of forces inside the nucleus. Two types of forces exist: (1) the long-range electrostatic (Coulomb) force that makes the positively charged protons repel one another; and (2) the short-range strong nuclear force    that makes all nucleons in the nucleus attract one another. You may also have heard of a “weak” nuclear force. This force is responsible for some nuclear decays, but as the name implies, it does not play a role in stabilizing the nucleus against the strong Coulomb repulsion it experiences. We discuss strong nuclear force in more detail in the next chapter when we cover particle physics. Nuclear stability occurs when the attractive forces between nucleons compensate for the repulsive, long-range electrostatic forces between all protons in the nucleus. For heavy nuclei $\left(Z>15\right),$ excess neutrons are necessary to keep the electrostatic interactions from breaking the nucleus apart, as shown in [link] .

Because of the existence of stable isotopes, we must take special care when quoting the mass of an element. For example, Copper (Cu) has two stable isotopes:

Given these two “versions” of Cu, what is the mass of this element? The atomic mass    of an element is defined as the weighted average of the masses of its isotopes. Thus, the atomic mass of Cu is $m_{\text{Cu}}=\left(62.929595\right)\left(0.6909\right)+\left(64.927786\right)\left(0.3091\right)=63.55\text{g/mol}.$ The mass of an individual nucleus is often expressed in atomic mass unit     s (u), where $\text{u}=1.66054\times {10}^{\mathrm{-27}}\text{kg}$ . (An atomic mass unit is defined as 1/12th the mass of a ${}^{12}\text{C}$ nucleus.) In atomic mass units, the mass of a helium nucleus ( A = 4 ) is approximately 4 u. A helium nucleus is also called an alpha ( α ) particle.

Nuclear size

The simplest model of the nucleus is a densely packed sphere of nucleons. The volume V of the nucleus is therefore proportional to the number of nucleons A , expressed by

where r is the radius of a nucleus    and k is a constant with units of volume. Solving for r , we have

where $r_0$ is a constant. For hydrogen ( $A=1$ ), $r_0$ corresponds to the radius of a single proton. Scattering experiments support this general relationship for a wide range of nuclei, and they imply that neutrons have approximately the same radius as protons. The experimentally measured value for $r_0$ is approximately 1.2 femtometer (recall that $1\text{fm}={10}^{\mathrm{-15}}\text{m}$ ).

Summary

• The atomic nucleus is composed of protons and neutrons.
• The number of protons in the nucleus is given by the atomic number, Z . The number of neutrons in the nucleus is the neutron number, N . The number of nucleons is mass number, A .
• Atomic nuclei with the same atomic number, Z , but different neutron numbers, N , are isotopes of the same element.
• The atomic mass of an element is the weighted average of the masses of its isotopes.

Conceptual questions

Problems