Question
Which of the following statements is false?
- The atomic number \(Z\) equals the number of protons in the nucleus of an atom.
- The mass number \(A\) equals the total number of protons plus neutrons in the nucleus.
- Isotopes of an element have the same atomic number but different mass numbers.
- For a neutral atom, the number of electrons equals the number of protons.
- The atomic mass shown on the periodic table is the mass of a single atom of the most abundant isotope of that element.
Answer
Statement E is false. The periodic-table atomic mass is a weighted average of the masses of naturally occurring isotopes, not the mass of one single atom of the most abundant isotope.
Why the other statements are true
| Statement | True/False | Justification (general chemistry definitions) |
|---|---|---|
| A | True | Atomic number \(Z\) is defined as the number of protons in the nucleus; changing \(Z\) changes the element identity. |
| B | True | Mass number \(A\) counts nucleons: \(A = (\text{protons}) + (\text{neutrons})\). Electrons are not included in \(A\). |
| C | True | Isotopes share the same number of protons (same \(Z\)) but differ in neutrons, so their \(A\) values differ. |
| D | True | A neutral atom has net charge \(0\), so total positive charge from protons equals total negative charge from electrons; therefore \(\#e^- = \#p^+\). |
| E | False | Periodic-table atomic mass is the weighted average over isotopes (using natural fractional abundances), typically not an integer. |
Correct idea behind atomic mass on the periodic table
If an element has isotopes with isotopic masses \(m_1, m_2, \dots\) (in atomic mass units, amu) and natural fractional abundances \(f_1, f_2, \dots\) (where \(f_1 + f_2 + \cdots = 1\)), then the periodic-table atomic mass is:
\[ \overline{m} = \sum_i \left(f_i \cdot m_i\right) \]Visualization: weighted average atomic mass using chlorine isotopes
Conclusion
The false statement is the claim that periodic-table atomic mass refers to a single isotope’s mass. In general chemistry, atomic mass is interpreted as a weighted average over isotopes, while atomic number, mass number, isotope identity, and neutrality follow directly from proton, neutron, and electron counting.