State the relation E = hf and E = hc/λ and define variables.

State the relation E = hf and E = hc/λ and define variables.

• A. E = h f = h c / λ; h is Planck's constant, f is frequency, c is the speed of light, λ is wavelength.
• B. E = f h / λ; h is Planck's constant, f is frequency, λ is wavelength.
• C. E = h c / f; h is Planck's constant, c is the speed of light, f is frequency.
• D. E = λ / (h f); h is Planck's constant, f is frequency, λ is wavelength.

Answer: (A)

Photon energy is determined by the frequency of the light, with Planck’s constant linking energy to frequency. The fundamental relation is E = hf, and because the frequency and wavelength are connected by the speed of light (f = c/λ), you can also write E = hc/λ. This shows the same energy expressed in terms of either frequency or wavelength. Definitions: - E: energy of a photon - h: Planck’s constant (≈ 6.626×10^-34 J·s) - f: frequency (cycles per second, Hz) - c: speed of light (≈ 3.00×10^8 m/s) - λ: wavelength (meters) The given form E = hf = hc/λ with those definitions is the correct and complete way to state the relationship. The other forms either mix the variables incorrectly or do not reflect the correct units and dependence on frequency or wavelength.

Photon energy is determined by the frequency of the light, with Planck’s constant linking energy to frequency. The fundamental relation is E = hf, and because the frequency and wavelength are connected by the speed of light (f = c/λ), you can also write E = hc/λ. This shows the same energy expressed in terms of either frequency or wavelength.

Definitions:

• E: energy of a photon

• h: Planck’s constant (≈ 6.626×10^-34 J·s)

• f: frequency (cycles per second, Hz)

• c: speed of light (≈ 3.00×10^8 m/s)

• λ: wavelength (meters)

The given form E = hf = hc/λ with those definitions is the correct and complete way to state the relationship. The other forms either mix the variables incorrectly or do not reflect the correct units and dependence on frequency or wavelength.