1.3.1 · D1Materials & Atomic Structure

Foundations — Bohr atomic model and electron shells

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Before you can read the Bohr page line by line, you need to already own every symbol it throws at you. Below, each symbol is introduced only after the one it depends on. We start from literally nothing — a charge, a distance — and build up to the boxed formulas.


1. Charge — the thing that pulls

Figure — Bohr atomic model and electron shells

The picture: two dots. Look at the red proton in the center and the black electron out to the side. The arrow points from electron toward proton — that is the pull. The whole Bohr model is a fight between this inward pull and the electron's tendency to fly off in a straight line.

Why the topic needs it: without charge there is no force, without force there is no orbit, without an orbit there is nothing to quantize.


2. Distance and radius — how far out

Why the topic needs it: the force gets weaker the farther apart the charges are, so how far matters enormously. The final boxed answer is literally a list of allowed distances.


3. The counting number —


4. Coulomb's constant — how strong the pull is

Figure — Bohr atomic model and electron shells

The picture: the red curve shows how the force shrinks as grows. Notice it drops fast — double the distance, quarter the force. That " on the bottom" is why.

Why the and not just ? Because the field spreads out over a sphere, and a sphere's surface grows as . This is the exact form Step 1 of the parent derivation uses.


5. Mass, speed, and the circle — ,

Figure — Bohr atomic model and electron shells

The picture: the electron on its circle, black arrow tangent (the direction it wants to fly), red arrow inward (the Coulomb pull that bends it into a circle). Step 1 of the derivation simply sets the pull = the required inward force.

Why the topic needs it: this balance is the entire Step 1 equation. Once you accept "inward force needed ," Coulomb's law fills in what supplies it.


6. Angular momentum — the quantized quantity

Why the topic needs it: this is Bohr's brand-new rule (Postulate 3). It is the mathematical form of "only certain orbits are allowed." Without it, could be anything.


7. Energy — kinetic, potential, total

Figure — Bohr atomic model and electron shells

The picture: the red energy-well curve. The bottom is the ground state (most negative, most trapped). The rungs climb toward zero as grows. This is the same picture behind .


8. Frequency, photons, and jumps — , ,

Why the topic needs it: this connects the invisible energy ladder to something you can see — spectral lines. Step 5 of the parent derivation is just this rule applied between two rungs.


9. Shells, capacity, and valence


Prerequisite map

Electric charge e

Coulomb force

Radius r

Mass m and speed v

Centripetal force

Force balance Step 1

Counting number n

Quantization L equals n hbar

Angular momentum L

Bohr radius r n

Energy levels E n

Kinetic and potential energy

Photon jumps delta E equals h f

Shells and capacity 2 n squared

Valence electrons and conductivity

Read it upward: charge and radius feed the Coulomb force; mass and speed feed the centripetal force; the two forces balance in Step 1; the counting number and angular momentum give the quantization rule; those two together produce the allowed radii, then the energy levels, then jumps and shells.


Equipment checklist

Cover the right side and check you can state each from memory.

What does the symbol stand for, and what sign does the electron carry?
is the size of one electron's charge; the electron is , the proton .
What does the subscript in mean?
The radius of the -th allowed orbit; is smallest.
What kind of number is , and what does "quantized" mean?
A whole counting number ; quantized means only these discrete values are allowed, nothing in between.
Read the bundle in plain words.
The "strength dial" for the electric (Coulomb) force; is the permittivity of free space.
Why does circular motion require a force, and what is its size?
Because direction constantly changes (acceleration); the required inward centripetal force is .
What is angular momentum for a circular orbit?
— mass times speed times radius.
What is ?
The reduced Planck constant , the natural chunk-size of angular momentum.
Why is a bound electron's total energy negative?
It sits below the "free" zero level in an energy well; you must add energy to free it.
What does describe?
A photon of energy emitted (or absorbed) when the electron jumps between rungs; is its frequency/color.
What is a valence electron and why care?
An electron in the outermost occupied shell; it decides bonding and electrical conductivity.
State the shell capacities for .
= 2, 8, 18, 32 (K, L, M, N).

Connections

  • Bohr atomic model and electron shells — the parent page these symbols unlock.
  • Atomic structure and the periodic table — where shells become periods and groups.
  • Valence electrons and bonding — the outermost-shell electrons in action.
  • Semiconductors and the band gap — why 4 valence electrons matter for Hardware.
  • Quantum mechanical model of the atom — the successor that refines these ideas.