Final answer:
The most stable number of neutrons for a cobalt atom with 27 protons is 41.
Step-by-step explanation:
In order for a cobalt atom to be most stable, it should have a specific ratio of neutrons to protons.
The ideal ratio of neutrons to protons for most atoms is approximately 1:1, but as the atomic number increases, the stable ratio gradually increases to about 1.5:1. For cobalt, with 27 protons, the most stable number of neutrons would be closest to 27 x 1.5 = 40.5.
Since atomic numbers and the number of protons are integers, the closest whole number to 40.5 is 41. Therefore, a cobalt atom with 27 protons would be most stable if it has 41 neutrons.