Question

which correctly describes how the energy of a wave on the electromagnetic spectrum depends on wavelength and frequency? a. energy increases with decreasing wavelength and increasing frequency. b. energy decreases with decreasing wavelength and decreasing frequency. c. energy decreases with increasing wavelength and increasing frequency. d. energy increases with decreasing wavelength and decreasing frequency.

Explanation:

The energy \( E \) of a photon (a particle of light, which is a type of electromagnetic wave) is given by the formula \( E = hf \), where \( h \) is Planck's constant (\( h>0 \)) and \( f \) is the frequency of the wave. Since \( h \) is a positive constant, \( E \) is directly proportional to \( f \) (as \( f \) increases, \( E \) increases). Also, the speed of light \( c \) is related to frequency \( f \) and wavelength \( \lambda \) by the formula \( c = f\lambda \) (\( c \) is a constant, \( c = 3\times10^{8}\ m/s \)). So, \( f=\frac{c}{\lambda} \). Substituting \( f=\frac{c}{\lambda} \) into \( E = hf \), we get \( E=\frac{hc}{\lambda} \). Since \( h \) and \( c \) are positive constants, \( E \) is inversely proportional to \( \lambda \) (as \( \lambda \) decreases, \( E \) increases).

Answer:

A. Energy increases with decreasing wavelength and increasing frequency.