Calculate the energy of a photon of each frequency and state what part of the electromagnetic spectrum is associated with the frequency.
a. 15.77×10¹⁷ Hz
b. 1.18×10¹⁴ Hz
c. 3.00×10²⁰ Hz

Verified step by step guidance

1. insert step 1: Use the formula for the energy of a photon, which is E = h \cdot f, where E is the energy, h is Planck's constant (6.626 \times 10^{-34} \text{ J}\cdot\text{s}), and f is the frequency.
2. insert step 2: For each frequency given, substitute the value of the frequency into the formula.
3. insert step 3: Calculate the energy for each frequency using the formula.
4. insert step 4: Identify the part of the electromagnetic spectrum each frequency corresponds to by comparing the frequency to known ranges for radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
5. insert step 5: State the energy calculated and the corresponding part of the electromagnetic spectrum for each frequency.

Key Concepts

Photon Energy Calculation

The energy of a photon can be calculated using the formula E = hν, where E is the energy, h is Planck's constant (6.626 × 10^-34 J·s), and ν (nu) is the frequency of the photon. This relationship shows that higher frequency photons have greater energy, which is crucial for understanding the behavior of electromagnetic radiation.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by frequency or wavelength. Different regions of the spectrum, such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, correspond to specific frequency ranges, influencing their applications and interactions with matter.

Frequency and Wavelength Relationship

Frequency (ν) and wavelength (λ) are inversely related through the equation c = λν, where c is the speed of light (approximately 3.00 × 10^8 m/s). This relationship indicates that as the frequency of electromagnetic radiation increases, its wavelength decreases, which is essential for identifying the part of the spectrum associated with a given frequency.