De Broglie's hypothesis and Bohr's atom

#### Bohr's first postulate

- Recall that Bohr postulated that electrons existed in distinct quantised orbits with an
**unexplainable stability.**- Typically an electron orbiting in a circle would emit EM radiation as it is accelerating.
- Bohr had no explanation for why this isn't so, but merely postulated that it just didn't.

- De Broglie's new hypothesis accounted for this by suggesting that the electrons exist as
**standing waves.**- This means they have a closed orbit with no
**movement of energy.** - Energy is instead constantly transferred between kinetic
**energy and potential energy**, but not lost.

- This means they have a closed orbit with no
- For this to occur:

\begin{align} 2 \pi r = n \lambda \end{align}

- Where n is an integer.

#### Bohr's third postulate

- Bohr postulated that the
**angular momentum of electrons were quantised**. - He had no basis for this, and it is only true if the equation $mvr = \frac{nh}{2\pi}$ was true.
- De Broglie's hypothesis was able to prove it, as shown below:

\begin{align} n \lambda =2 \pi r \end{align}

Using matter waves ($\lambda = \frac{h}{mv}$):

(3)\begin{align} \frac{nh}{mv} =2 \pi r \end{align}

Rearranging:

(4)\begin{align} mvr = \frac{nh}{2\pi} \end{align}

- Thus de Broglie's hypothesis had been able to explain Bohr's postulates and validify his model of the atom.

page revision: 2, last edited: 03 Nov 2011 07:08