# Atomic radius: nearly constant

> Two opposite factors in balance


## Objectives

- Read the atomic radius column: little change across the series, nearly constant from Cr to Cu.
- Explain it with the book's two opposite factors: effective nuclear charge and repulsion between 3d electrons.
- Contrast it with the clear decrease across a period of representative elements.

## 1. General properties: mass, radius and metallic property




## 2. Shrink or stay?

Predict: what happens to the atomic radius from Cr to Cu?

- It increases clearly
- It falls sharply, as across period 3
- It stays nearly constant ✓

From Cr to Cu the atomic radius stays nearly constant: the growing nuclear attraction is opposed by the growing repulsion between the 3d electrons.

[ar-EG] من الـ Cr للـ Cu الـ atomic radius بيفضل ثابت تقريبًا: الـ nuclear attraction اللي بتزيد بيعاكسها التنافر اللي بيزيد بين الـ 3d electrons.
## 3. The atomic radius column

Atomic radius from Sc to Cu (book's table, p.12, for illustration only) Book point 2: the atomic radius changes **little** across the first transition series. From Cr to Cu it is **nearly constant**: 1.17, 1.17, 1.16, 1.16, 1.15, 1.17.


## 4. Factor 1: a stronger pull

Effective nuclear charge The pull of the nucleus that the outer electrons actually feel. From Sc to Cr, the effective nuclear charge increases. The nuclear attraction to electrons increases. This factor **decreases** the atomic radius. Acting alone, it would keep shrinking the atoms. Factor 1 from Sc to Cr


## 5. Factor 2: 3d electrons repel

Two opposite factors act on the size of the atom From Sc to Cu, the number of 3d electrons grows from 1 to 10. More 3d electrons repel each other more. This factor **increases** the atomic radius. The two factors oppose each other, so the radius stays relatively constant.


## 6. Watch the size

Move from Sc to Cu. Watch the 3d electrons grow while the atom stops shrinking. element (1 = Sc … 9 = Cu) $\ce{Sc}$: $[\text{Ar}]\ 4s^2\ 3d^1$. The first element: the largest radius here. atomic radius (book) electrons in 3d $\ce{Ti}$: $[\text{Ar}]\ 4s^2\ 3d^2$. The pull wins: the radius falls. atomic radius (book) electrons in 3d $\ce{V}$: $[\text{Ar}]\ 4s^2\ 3d^3$. The pull wins: the radius falls. atomic radius (book) electrons in 3d $\ce{Cr}$: $[\text{Ar}]\ 4s^1\ 3d^5$. The two factors start to balance. atomic radius (book) electrons in 3d $\ce{Mn}$: $[\text{Ar}]\ 4s^2\ 3d^5$. The two factors balance: nearly constant. atomic radius (book) electrons in 3d $\ce{Fe}$: $[\text{Ar}]\ 4s^2\ 3d^6$. The two factors balance: nearly constant. atomic radius (book) electrons in 3d $\ce{Co}$: $[\text{Ar}]\ 4s^2\ 3d^7$. The two factors balance: nearly constant. atomic radius (book) electrons in 3d $\ce{Ni}$: $[\text{Ar}]\ 4s^2\ 3d^8$. The two factors balance: nearly constant. atomic radius (book) electrons in 3d $\ce{Cu}$: $[\text{Ar}]\ 4s^1\ 3d^{10}$. The two factors balance: nearly constant. atomic radius (book) electrons in 3d


## 7. Remove one factor

Imagine the 3d electrons did not repel each other. What would the radius do from Cr to Cu?

- Keep decreasing, as across period 3 ✓
- Increase
- Stay nearly constant, as in the table

Without the repulsion between the 3d electrons, the growing nuclear attraction would act alone, so the radius would keep decreasing, as across period 3.

[ar-EG] من غير التنافر بين الـ 3d electrons، الـ nuclear attraction اللي بتزيد هتشتغل لوحدها، فالـ radius هيفضل يقل، زي ما بيحصل في period 3.
## 8. Build the exam answer

Give reasons: the atomic radius is nearly constant from Cr to Cu. Put the answer in order.


## 9. Summary

The atomic radius changes little; it is nearly constant from Cr to Cu. Effective nuclear charge increases: the radius tends to decrease. More 3d electrons repel more: the radius tends to increase. The book adds: this explains their use in making alloys. An alloy is a metal mixed with other elements; you will study it later. Two **opposite factors**: the **effective nuclear charge increases** (radius decreases), while the **repulsion between 3d electrons increases** (radius increases). So the atomic radius is **relatively constant**. Can you explain why these atoms stop shrinking, though each gains a proton? Each extra proton raises the effective nuclear charge, which would decrease the radius. But the number of 3d electrons grows too, and their repulsion would increase the radius. The two opposite factors balance, so the radius is nearly constant from Cr to Cu.



Chapter: Transition Elements (https://yaani.ai/ar/learn/chemistry/chem-s3-en.ch1)
Source: https://yaani.ai/ar/lesson/chem-s3-en.lesson-te.atomic-radius