Question

which of the following statements accurately describe the wave properties of light? (select all that apply)
as the frequency of light increases, its wavelength also increases.
the speed of light varies with the frequency of the wave in a vacuum.
the energy of a light wave is directly proportional to its frequency.
light with a shorter wavelength has a higher energy than light with a longer wavelength.
the wavelength of light is inversely proportional to its frequency.
the speed of light in a vacuum is a constant value, approximately 3.00 × 10⁸ meters per second.

Explanation:

Step1: Analyze the relationship between frequency and wavelength

The formula \(c = \lambda
u\) (where \(c\) is the speed of light, \(\lambda\) is wavelength, and \(
u\) is frequency) shows that \(\lambda=\frac{c}{
u}\). So, as frequency \(
u\) increases, wavelength \(\lambda\) decreases. The statement “As the frequency of light increases, its wavelength also increases” is wrong.

Step2: Consider the speed of light in vacuum

The speed of light \(c\) in a vacuum is a constant (\(c = 3.00\times10^{8}\space m/s\)). The formula \(c=\lambda
u\) implies that when \(c\) is constant (in vacuum), \(\lambda\) and \(
u\) are inversely proportional. The statement “The speed of light varies with the frequency of the wave in a vacuum” is wrong.

Step3: Examine the energy - frequency relationship

The energy of a photon (light wave) is given by \(E = h
u\) (where \(h\) is Planck’s constant). So, energy \(E\) is directly proportional to frequency \(
u\). The statement “The energy of a light wave is directly proportional to its frequency” is correct.

Step4: Relate wavelength and energy

Since \(E = h
u\) and \(c=\lambda
u\) (\(
u=\frac{c}{\lambda}\)), then \(E=\frac{hc}{\lambda}\). So, shorter wavelength (\(\lambda\)) means higher energy (\(E\)). The statement “Light with a shorter wavelength has a higher energy than light with a longer wavelength” is correct.

Step5: Check the wavelength - frequency relationship

From \(c = \lambda
u\) (\(\lambda=\frac{c}{
u}\)), wavelength \(\lambda\) is inversely proportional to frequency \(
u\). The statement “The wavelength of light is inversely proportional to its frequency” is correct.

Step6: Verify the speed of light in vacuum

The speed of light in a vacuum \(c = 3.00\times 10^{8}\space m/s\) is a fundamental constant. The statement “The speed of light in a vacuum is a constant value, approximately \(3.00\times 10^{8}\) meters per second” is correct.

Answer:

The correct statements are:

• The energy of a light wave is directly proportional to its frequency.
• Light with a shorter wavelength has a higher energy than light with a longer wavelength.
• The wavelength of light is inversely proportional to its frequency.
• The speed of light in a vacuum is a constant value, approximately \(3.00\times 10^{8}\) meters per second.