Final answer:
Approximately 1200 electrons must be added to the brass key to make it electrically neutral. The charge on the brass key is not due to the excess of protons. If the key gains additional positive charge, it will require more electrons to neutralize it.
Step-by-step explanation:
An electron carries a negative charge of -1.6 x 10^(-19) C, while a proton carries a positive charge of +1.6 x 10^(-19) C. To make an object electrically neutral, the number of electrons needed is equal to the net positive charge divided by the charge per electron. In this case, the brass key has a positive charge of +1.92 x 10^(-16) C, so the number of electrons needed is calculated as:
Number of electrons = (1.92 x 10^(-16) C) / (1.6 x 10^(-19) C per electron)
Number of electrons = 1.2 x 10^3 electrons
Therefore, approximately 1.2 x 10^3 electrons must be added to the key to make it electrically neutral. Answer choice B, 1.92 x 10^16 electrons, is incorrect because it implies a much greater number of electrons than necessary.
The charge on the brass key is not due to the excess of protons. Rather, it has gained a net positive charge due to some external influence. Answer choice B, False, is the correct answer.
If the key gains additional positive charge, it will require more electrons to neutralize it. The net positive charge on the key will increase, and therefore the number of electrons needed to balance the charge will also increase. Answer choice A, More electrons needed, is the correct answer.