The number of elements in each period of the periodic table can be determined by a simple formula based on the period number. Each period ends with a rare gas element, such as Helium or Neon, and the number of elements in a period can be calculated using the formula: L = 2n^2, where n is the period number and L is the number of elements in that period. This formula helps us understand how many elements are present in each row of the periodic table based on its position.