The density of an element is directly related to its atomic mass and inversely related to its atomic volume. Bromine and iodine have higher atomic masses than fluorine and chlorine, and smaller atomic volumes. This means that bromine and iodine are more densely packed than fluorine and chlorine, resulting in their higher densities.

Here's a more detailed explanation:

1. Atomic Mass: The atomic mass of an element is the sum of the protons and neutrons in its nucleus. Bromine has an atomic mass of 79.904, while iodine's atomic mass is 126.904. In comparison, fluorine has an atomic mass of 18.998 and chlorine has an atomic mass of 35.453.

2. Atomic Volume: The atomic volume is the amount of space occupied by one mole of an element in its solid state. Bromine has an atomic volume of 20.6 cm³/mol, while iodine's atomic volume is 25.7 cm³/mol. On the other hand, fluorine has an atomic volume of 16.9 cm³/mol, and chlorine has an atomic volume of 25.7 cm³/mol.

Comparing these values, we can see that bromine and iodine have higher atomic masses and smaller atomic volumes compared to fluorine and chlorine. This results in bromine and iodine being more densely packed, leading to their higher densities.