Question:

Consider a nucleus with atomic number Z and mass number A.

a) Define atomic number and mass number. b) What is the total number of protons and neutrons in the nucleus? c) If the nucleus contains Z protons and A - Z neutrons, what is the atomic mass of the nucleus in atomic mass units (amu)? d) If the nucleus undergoes alpha decay, what are the resulting atomic number and mass number?

Answer:

a) Atomic number (Z) refers to the number of protons in the nucleus of an atom. It determines the element's identity and its position in the periodic table. The mass number (A) represents the total number of protons and neutrons in the nucleus.

b) The total number of protons and neutrons in the nucleus is equal to the mass number (A).

c) If the nucleus contains Z protons and A - Z neutrons, the atomic mass of the nucleus can be calculated by summing the masses of individual protons and neutrons. The mass of a proton is approximately 1 atomic mass unit (amu), and the mass of a neutron is also approximately 1 amu. Therefore, the atomic mass (M) of the nucleus can be calculated using the formula:

M = (Z * m_proton) + ((A - Z) * m_neutron)

where m_proton and m_neutron are the masses of proton and neutron, respectively, both equal to 1 amu.

Let's substitute the values into the formula:

M = (Z * 1 amu) + ((A - Z) * 1 amu)

Simplifying further:

M = Z amu + (A - Z) amu

M = A amu

Therefore, the atomic mass of the nucleus is equal to the mass number and is measured in atomic mass units (amu).

d) Consider an alpha decay, where an alpha particle (helium nucleus, 4He) is emitted from the nucleus. In this process, the mass number (A) is decreased by 4, and the atomic number (Z) is decreased by 2. Therefore, the resulting atomic number (Z') and mass number (A') can be calculated as follows:

Z' = Z - 2 A' = A - 4

The resulting atomic number would decrease by 2, and the resulting mass number would decrease by 4 due to the ejection of an alpha particle.