Question

how are wavelength, frequency, and energy related?
a a longer wavelength means higher frequency and higher energy.
b a longer wavelength means higher frequency and lower energy.
c a longer wavelength means lower frequency and higher energy.
d a longer wavelength means lower frequency and lower energy.

Explanation:

Step1: Relationship between wavelength and frequency

The formula \(c = \lambda
u\) (where \(c\) is the speed of light, \(\lambda\) is wavelength, and \(
u\) is frequency) shows that \(\lambda\) and \(
u\) are inversely proportional (\(
u=\frac{c}{\lambda}\)). So, a longer wavelength (\(\lambda\)) means a lower frequency (\(
u\)).

Step2: Relationship between frequency and energy

The formula \(E = h
u\) (where \(E\) is energy and \(h\) is Planck's constant) shows that \(E\) and \(
u\) are directly proportional. Since a longer wavelength gives lower \(
u\), from \(E = h
u\), lower \(
u\) means lower \(E\).

Answer:

D. A longer wavelength means lower frequency and lower energy.