To determine the atomic number of the alkaline earth metal in the eighth period, we need to understand the periodic table and the arrangement of elements in the periodic table.

- Periods in the periodic table represent the different energy levels or shells in an atom. The seventh period is the period that contains the elements from atomic number 87 (francium) to atomic number 118 (oganesson).

- Alkaline earth metals are located in Group 2 of the periodic table. This group includes the elements beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra).

- As we move down a group in the periodic table, the atomic number increases by one. For example, magnesium has an atomic number of 12, calcium has an atomic number of 20, and so on.

- The eighth period would be the period after the seventh period, and it would contain elements with higher atomic numbers than the elements in the seventh period.

Now, let's analyze the given options:

a) 113: This is the atomic number of element Nihonium (Nh), which belongs to the 7th period, not the 8th period. So, option a) is incorrect.

b) 120: This is the correct answer. If we assume that elements are formed to complete the seventh period, the alkaline earth metal of the eighth period would have an atomic number of 120. However, it's important to note that as of now, there are no elements discovered with an atomic number of 120.

c) 119: This is the atomic number of element Ununennium (Uue), which belongs to the 7th period, not the 8th period. So, option c) is incorrect.

d) 106: This is the atomic number of element Seaborgium (Sg), which belongs to the 7th period, not the 8th period. So, option d) is incorrect.

In conclusion, the correct answer is option b) 120, although there are currently no elements discovered with that atomic number.