There are 4 atoms in the unit cell of titanium metal.

Explanation:

- Define the unit cell: The unit cell is the smallest repeating unit of a crystal lattice structure. In this case, we are considering the unit cell of titanium metal.

- Determine the edge length: The given information states that the edge length of the unit cell is 412.6 pm (picometers).

- Convert the edge length to cm: To work with consistent units, we need to convert the edge length from pm to cm. 1 pm is equal to 1 × 10^-10 cm. Therefore, 412.6 pm is equal to 412.6 × 10^-10 cm.

- Calculate the volume of the unit cell: The volume of a cube is given by the formula V = a^3, where 'a' is the length of one edge. Plugging in the edge length, we have V = (412.6 × 10^-10 cm)^3.

- Convert the density to g/cm^3: The information also provides the density of titanium metal, which is 4.54 g cm^-3.

- Calculate the mass of the unit cell: The mass of the unit cell can be calculated using the formula m = ρV, where 'ρ' is the density and 'V' is the volume. Plugging in the values, we have m = 4.54 g cm^-3 × V.

- Determine the molar mass of titanium: The molar mass of titanium (Ti) is given as 48 g/mol.

- Calculate the number of moles: The number of moles can be calculated using the formula n = m/M, where 'm' is the mass and 'M' is the molar mass. Plugging in the values, we have n = m/48 g/mol.

- Determine the number of atoms: The number of atoms in the unit cell can be calculated using Avogadro's number (6.022 × 10^23 atoms/mol). The number of atoms is equal to n × Avogadro's number.

- Calculate the final answer: Plugging in the values, we have n × 6.022 × 10^23 atoms/mol.

- Simplify the answer: The final answer is 4, which means there are 4 atoms in the unit cell of titanium metal.

Therefore, the correct answer is '4'.