Question

What type of relationship (direct or inverse) exists between wavelength, frequency, and photon energy? What does a photon energy unit of a joule equal?

Short answer

An inverse relationship exists between wavelength and frequency, as well as between wavelength and photon energy. A direct relationship exists between frequency and photon energy. A photon energy unit of one joule (J) represents the energy carried by a single photon, with 1 J being equal to 1 newton-meter (Nm).

Step-by-step solution

Relationship between wavelength and frequency

The wavelength (λ) and frequency (ν) of a wave are related by the formula: \[ c = λν \] where \(c\) is the speed of light in a vacuum (\(3.0 × 10^8\) m/s). Since the speed of light is a constant, the relationship between the wavelength and frequency is an inverse one: As the wavelength of a wave increases, its frequency decreases, and vice versa.

Relationship between photon energy and frequency

The energy of a photon (E) is related to its frequency (ν) by the formula: \[ E = hν \] where \(h\) is the Planck constant (\(6.626 × 10^{-34}\) Js). The relationship between photon energy and frequency is a direct one: As the frequency of a wave increases, its energy also increases, and vice versa.

Relationship between photon energy and wavelength

Combining the equations for the speed of light and the energy of a photon gives us an equation that relates photon energy with wavelength: \[ E = \frac{hc}{λ} \] Here, the relationship between photon energy and wavelength is an inverse one: As the wavelength of a wave increases, its energy decreases, and vice versa.

Photon energy unit of a joule

A joule (J) is the unit of energy in the International System of Units (SI) and is defined as the amount of work done when a force of one newton is applied over a distance of one meter in the direction of the force: \[ 1 J = 1 Nm \] In the context of this problem, photon energy is also given in joules. Therefore, a photon energy unit of one joule represents the energy that a single photon carries.