Constants & Equations

Equation

Name & Meaning

Notes

E = hf

Planck’s equation

Photon energy = Planck’s constant × photon frequency

 

Question

If an electron changes energy levels from 5.00 × 10-20 Joules to 4.00 × 10-20 Joules, and transfers the energy it loses to a photon, what will be the frequency of the photon?

 

Answer

The change in energy of the electron,

ΔE = (4.00 – 5.00) × 10-20.

ΔE = -1.00 × 10-20 J.

The change in energy is negative because the electron loses energy.  The photon emitted will gain the energy lost by the electron.

Therefore the energy of the photon is the same value and the opposite sign of the change in energy of the electron:

E = -ΔE (of electron).

E = - (-1.00 × 10-20) = 1.00 × 10-20 J

 

Use Planck’s equation:

E = hf

Divide both sides by h to make frequency the subject of the expression:

E / h = f

Enter the values of E and h into the expression, then use a calculator to find the answer:

f = E / h = (1.00 × 10-20) / (6.63 × 10-34)

 = 1.51 × 1013 Hz

Planck’s constant, h = 6.63 × 10-34 JHz-1

 

Frequency may be represented by the letter f or by the Greek letter ν (called Nu, pronounced noo) – if ν is used, the expression becomes E = hν.  It still has the same meaning.

Ka

Acid dissociation constant

HA is a weak acid (only a small percentage of its molecules dissociate into hydrogen ions and anions).  It dissociates into a hydrogen ion H+ and its conjugate base A-.

 

The acid dissociation constant for weak acids is a special case of an equilibrium constant.  It is derived from the expression for Kc and the equilibrium reaction HA(aq)  H+(aq) + A-(aq).

 

Kw

The ionic product of water

 

Kw = [H+(aq)] [OH-(aq)]

 

Kw = 1.00 × 10-14 mol2dm-6 at 298K

 

Ionic product of water = concentration of hydrogen ions × concentration of hydroxide ions

 

(All concentrations in moles per litre, mol dm-3)

 

The ionic product of water is a special modification of an equilibrium constant, called the acid dissociation constant of water.

 

The acid dissociation constant of water is a more complicated expression than is necessary because the concentration of water can be treated as constant as it is always in excess.