Balancing Nuclear Charge for Atomic Number 103

The question asks what balances the nuclear charge of an element with atomic number 103, given that its nuclear charge is +103.

Let's break down the key concepts:

• Atomic Number: The atomic number of an element is equal to the number of protons in the nucleus of an atom of that element. In this case, the atomic number is 103, which means the element has 103 protons.
• Nuclear Charge: The nucleus of an atom contains protons and neutrons. Protons are positively charged, while neutrons have no charge. The nuclear charge is the total positive charge of all the protons in the nucleus. Since each proton has a charge of +1, 103 protons result in a nuclear charge of $103 \times (+1) = +103$. The question states the nuclear charge is +103, which aligns with the atomic number.
• Balancing Charge: For an atom to be electrically neutral (have no net charge), the total positive charge must be equal to the total negative charge. The negative charge in an atom comes from the electrons, which orbit the nucleus. Each electron has a charge of -1.

To balance a nuclear charge of +103, we need a total negative charge of -103. Since each electron has a charge of -1, the number of electrons required is:

Number of electrons $= \frac{\text{Total negative charge}}{\text{Charge per electron}} = \frac{-103}{-1} = 103$

Therefore, to balance the nuclear charge of +103 and make the atom neutral, there must be 103 electrons.

Let's look at the options:

• Option 1: 103 electrons. This provides a total charge of $103 \times (-1) = -103$, which balances the +103 nuclear charge.
• Option 2: 103 protons. Protons are in the nucleus and contribute to the positive nuclear charge; they do not balance it from outside the nucleus.
• Option 3: 104 electrons. This would provide a total charge of $104 \times (-1) = -104$, resulting in a net charge of $+103 + (-104) = -1$ (a negatively charged ion).
• Option 4: 104 protons. The number of protons determines the element. If there were 104 protons, the atomic number would be 104, not 103.

The charge of +103 from the nucleus (due to 103 protons) is balanced by the charge from 103 electrons, each carrying a -1 charge, resulting in a neutral atom.