Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)

검증된 단계별 안내

Convert the wavelength from nanometers (nm) to meters (m) by multiplying by \(1 \times 10^{-9}\) m/nm.

Use the speed of light equation, \(c = \lambda \nu\), where \(c\) is the speed of light (\(3.00 \times 10^8\) m/s), \(\lambda\) is the wavelength in meters, and \(\nu\) is the frequency in Hz.

Rearrange the equation to solve for frequency, \(\nu = \frac{c}{\lambda}\).

Substitute the converted wavelength value into the rearranged equation to calculate the frequency for each case.

Ensure the final frequency is expressed in hertz (Hz), which is the SI unit for frequency.

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주요 개념

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Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which vary in wavelength and frequency. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Understanding the spectrum is crucial for identifying the properties and applications of different types of radiation, such as the visible light emitted by lasers or the X-rays used in medical imaging.

Wavelength and Frequency Relationship

Wavelength and frequency are inversely related properties of electromagnetic radiation, described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This means that as the wavelength increases, the frequency decreases, and vice versa. This relationship is fundamental for calculating the frequency of radiation given its wavelength, as seen in the question.

Unit Conversion

In calculations involving electromagnetic radiation, it is often necessary to convert units, particularly when dealing with wavelengths expressed in nanometers (nm) and frequencies in hertz (Hz). One nanometer equals 1 x 10^-9 meters, and frequency is typically expressed in hertz, which is cycles per second. Mastery of unit conversion is essential for accurately performing calculations and interpreting results in physics and chemistry.