Final answer:
Based on the principles of conservation of charge and charge quantization, the charge on the third object can be calculated by considering the total charge of the system and the charges on the first two objects.
Step-by-step explanation:
The question is based on the concept of the conservation of charge and charge quantization. Conservation of Charge implies that the total charge within an isolated system will remain constant regardless of the individual movements and reactions within the system. In your case, the spherical shell with three charged objects will have a total charge that is the sum of the charges of the three objects. Charge quantization implies that the charge on a body is always an integral multiple of the elementary charge, which is 1.6*10^-19 Coulombs, the charge on a single electron or proton.
Given that the first object has a charge of -16.0 nC and the second has a charge of 34.0 nC, based on conservation of charge, the charge on the third object can be calculated by adding the charges of the first two objects and taking this value from the total charge of the system. If the options given are possible total charges of the system, you can calculate the charge on the third object. For instance, with a total charge of -50.0 nC (option 1), the charge on the third object would be -50.0 nC - (-16.0 nC) - 34.0 nC = -68.0 nC. The same can be calculated for the other options.
Remember, the number of electrons ne is the total charge divided by the charge per electron.
Learn more about Conservation of Charge