What is the relationship between wavelengths and energy?

Answer 1

The amount of energy is inversely related to the wavelength of the radiation: the shorter the wavelength, the greater the energy of each photon.

This was originally discovered by Max Planck who identified a co-effiecient of proportionality that related a photon's energy to its frequency. This co-effiecient is known as the Planck constant and allows the energy of a photon to be found using the following relation (known as the Planck relation or the Planck-Einstein equation):

E = hv (Eq. 1)

Where:

E = Energy (J)

h = Planck constant (6.62606896×10−34 Js)

v = frequency (Hz).

For electromagnetic radiation travelling through a vacuum:

v = c / λ(Eq. 2)

Where:

c = speed of light in a vacuum

λ = wavelength (m)

As such this can be substituted into the Planck relation to give the following: E = hc / λ(Eq. 3)

From equations 1 and 3 it can be seen that a photon's energy is directly proportional to it's frequency and inversely proportional to its wavelength.

Answer 2

What kind of wave? There are significant difference, for example, between water waves, sound waves, or electromagnetic waves.

Answer 3

Energy of a particular electromagnetic wave is inversely proportional to it's wavelength.

As per Planck's quantum theory energy emitted by a body is not continuous but in the form of packets called quantum(in plural quanta). The energy associated with each quantum of a given radiation is directly proportional to frequency and inversely proportional to wavelength of the emitted radiation.

energy = Planck's constant * frequency.

E=h*f

or, E = h*c/ w.

where E is energy of emitted radiation, f is frequency, w is wavelength of emitted radiation, and c is speed of light.

Planck's constant 'h' = 6.624 * 10-34 Joule *sec