What wavelength of electromagnetic radiation corresponds to...

What wavelength of electromagnetic radiation corresponds to a frequency of $7.76 \times 10^{9} \mathrm{~s}^{-1}$ ? Note that Planck's constant is $6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}$, and the speed of light is $3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$.

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Key Concepts

Relationship between Frequency, Wavelength, and Speed of Light

The fundamental relationship between frequency, wavelength, and the speed of light is given by the equation c = ??, where c is the constant speed of light in a vacuum, ? (wavelength) is the distance between successive wave peaks, and ? (frequency) is the number of wave cycles per second. This equation is essential for understanding how changes in frequency impact wavelength and vice versa, illustrating the inverse relationship between these two quantities in electromagnetic waves.

Electromagnetic Radiation

Electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space at the speed of light. These waves encompass a broad spectrum that includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The properties of electromagnetic radiation are determined by characteristics such as wavelength and frequency, which define its position within the spectrum.

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