To determine the amount of cobalt to be added to a material if the required number of atoms is 50500, you need to consider the molar mass of cobalt and Avogadro's number.
Find the molar mass of cobalt (Co): The molar mass of cobalt is approximately 58.93 grams per mole (g/mol). This value represents the average mass of one mole of cobalt atoms.
Use Avogadro's number: Avogadro's number (6.022 × 10^23) represents the number of atoms or molecules in one mole of a substance.
Now, let's calculate the amount of cobalt needed:
Amount of cobalt (in moles) = Number of atoms / Avogadro's number = 50500 / (6.022 × 10^23)
To convert the amount from moles to grams, we multiply by the molar mass of cobalt:
Amount of cobalt (in grams) = Amount of cobalt (in moles) × Molar mass of cobalt = (50500 / (6.022 × 10^23)) × 58.93
The significance of this answer lies in determining the precise amount of cobalt required to meet the specified number of atoms (50500 in this case). By calculating the mass of cobalt needed, you can ensure that the desired quantity is added to the material accurately, maintaining the intended properties or characteristics associated with cobalt incorporation. This level of precision is essential in various fields, including materials science, chemistry, and manufacturing processes, where the exact composition of a material can significantly affect its performance or properties.