Math Problem Statement

What is the energy of a photon of light whose frequency is 6.91 x 10^15 Hz?

Solution

The energy EE of a photon can be calculated using the equation:

E=hfE = h \cdot f

where:

  • EE is the energy of the photon,
  • hh is Planck's constant (6.626×1034J\cdotps6.626 \times 10^{-34} \, \text{J·s}),
  • ff is the frequency of the photon.

Given:

  • f=6.91×1015Hzf = 6.91 \times 10^{15} \, \text{Hz}

Substituting the values into the equation:

E=(6.626×1034J\cdotps)(6.91×1015Hz)E = (6.626 \times 10^{-34} \, \text{J·s}) \cdot (6.91 \times 10^{15} \, \text{Hz})

Let's calculate it:

E=4.579×1018JE = 4.579 \times 10^{-18} \, \text{J}

So, the energy of the photon is approximately 4.579×1018J4.579 \times 10^{-18} \, \text{J}.

Would you like more details or have any questions?

Here are five related questions you could explore:

  1. What is the relationship between wavelength and frequency in light?
  2. How does photon energy relate to the color of visible light?
  3. What is the wavelength of a photon with the given frequency?
  4. How is the photoelectric effect related to photon energy?
  5. How does photon energy change with frequency?

Tip: Higher frequency photons, like X-rays and gamma rays, carry more energy than lower frequency photons, such as visible light or radio waves.

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Math Problem Analysis

Mathematical Concepts

Physics
Photon Energy
Frequency

Formulas

E = h · f (Energy of a photon formula)

Theorems

Planck's Equation

Suitable Grade Level

Grades 11-12