Atomic core charge in a neutral copper (Cu) atom In solid-state physics, the 'ion core' (or atomic core) is defined as the nucleus plus all core (non-valence) electrons. For a neutral copper atom (atomic number 29), where the single 4s electron is considered valence, what is the net charge of the remaining core?

Introduction / Context:
In materials science and solid-state physics, we often separate a neutral atom into a positively charged “ion core” (nucleus plus core electrons) and the outer valence electrons that participate in bonding and conduction. This partition helps in building pseudopotentials and explaining electron behavior in metals and semiconductors. For copper (Cu), recognizing the charge state of the core is a key first step.

Given Data / Assumptions:

• Copper atomic number Z = 29.
• Neutral atom has total electron charge −29 e and nuclear charge +29 e.
• Valence configuration of Cu is typically taken as 4s^1 (one valence electron).
• “Core” = nucleus (+29 e) + 28 core electrons (−28 e) = ion core used in many models.

Concept / Approach:

The ion-core concept removes the valence electron(s) from the neutral atom and groups the remainder into an effective core. The core's net charge is the nuclear charge minus the charge of all core electrons. Because a neutral Cu atom has one valence electron outside the core, the core must be net positive by +1 e to balance the missing valence charge when reconstructing neutrality.

Step-by-Step Solution:

Verification / Alternative check:

If we recombine the +1 e core with the one valence electron (−1 e), total returns to zero, confirming neutrality. This convention is standard in pseudopotential and nearly-free-electron treatments for Cu-based metals and alloys.

Why Other Options Are Wrong:

0 would mean no net core charge, contradicting the definition that removes one valence electron. −1 or −2 would imply the core is negative, which cannot balance neutrality when the valence electron is also negative. +2 would correspond to removing two valence electrons, not appropriate for elemental Cu with one 4s valence electron in this model.

Common Pitfalls:

Confusing “ion core” with an ionic oxidation state in chemistry; here it is a modeling construct, not the chemical Cu^+ ion in a compound.

Final Answer:

+1