As wavelength decreases, energy ?

For light, the energy (of a photon) is inversely proportional to wavelength. Light consists of massless particles called photons.

For sound, water and other types of matter waves, amplitude and speed determine wave power.

The one-word answer they probably want is "increases".

To understand the relationship between wavelength and energy, we need to consider the concept of electromagnetic waves. Electromagnetic waves include all forms of light, ranging from radio waves with long wavelengths to gamma rays with very short wavelengths.

The energy of an electromagnetic wave is directly proportional to its frequency, denoted by the symbol ν (nu). Frequency is the number of complete wave cycles that pass a given point in one second. The relationship between frequency and wavelength is described by the equation:

ν = c / λ

Where:
ν = frequency
c = speed of light (approximately 3 x 10^8 meters per second)
λ = wavelength

From this equation, we can determine that as wavelength (λ) decreases, the frequency (ν) increases.

Energy (E) is directly proportional to frequency, and it can be calculated using Planck's equation:

E = h * ν

Where:
E = energy
h = Planck's constant (approximately 6.626 x 10^-34 joule-seconds)
ν = frequency

Since the frequency increases as the wavelength decreases, according to the relationship ν = c / λ, we can conclude that as the wavelength decreases, the energy increases. This means that shorter wavelengths, such as gamma rays or X-rays, have higher energy compared to longer wavelengths like radio waves or infrared radiation.