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Question: Calculate (a) frequency and (b) wave-number of yellow radiation having wavelength \(5800\mathop A\li...

Calculate (a) frequency and (b) wave-number of yellow radiation having wavelength 5800Ao5800\mathop A\limits^o .

Explanation

Solution

Frequency is the number of times a wave is passing through an area per unit time. These are applied in sound, radio, and light. Wavelength is the distance between successive crests of a wave. Wavenumber is the reciprocal of the wavelength. Examples of waves are sound, electromagnetic waves such as light, radio, water waves from the ocean, and earthquake waves. The yellow region is found between green and orange on the spectrum of visible light. Sodium light produces a yellow wavelength.

Complete step by step answer:
Frequency is defined as the number of waves passing through a particular point at a period. By knowing the wavelength of the particular compound, the frequency can be determined.
Given, the wavelength of the light is 5800Ao5800\mathop A\limits^o = 5800 x 10−10m5800{\text{ }}x{\text{ }}{10^{ - 10}}m
Frequency = cwavelength=\dfrac{c}{{wavelength}} = 3 x 1085800 x 10−10=0.05 x 1016\dfrac{{3{\text{ }}x{\text{ 1}}{{\text{0}}^8}}}{{5800{\text{ }}x{\text{ 1}}{{\text{0}}^{ - 10}}}} = 0.05{\text{ }}x{\text{ 1}}{{\text{0}}^{16}}
Whereas the wavenumber can be determined by using the wavelength, the wavenumber is inversely proportional to the wavelength.
Wavenumber = 1wavelength\dfrac{1}{{wavelength}}= 15800 x 10−10\dfrac{1}{{5800{\text{ }}x{\text{ }}{{10}^{ - 10}}}}= 0.017 x 108m−10.017{\text{ }}x{\text{ }}{10^8}{m^{ - 1}}
Therefore, the frequency of the yellow radiation of 5800Ao5800\mathop A\limits^o is0.05 x 10160.05{\text{ }}x{\text{ 1}}{{\text{0}}^{16}} and the wavenumber is 0.017 x 108m−10.017{\text{ }}x{\text{ }}{10^8}{m^{ - 1}}.

Note:
The SI unit for frequency is the Hertz (Hz), which is equivalent to the older unit cycles per second (cps). Frequency is also known as cycles per second or temporal frequency. Examples of frequency is the frequency of heartbeat per minute. A 28 record on a turntable turns at the rate of 28 revolutions per minute or 28 rpm. The wavelength of yellow light is 240×10−9m240 \times {10^{ - 9}}m. The SI unit of wavelength is meter. The wavenumber of yellow light4.16×106m−14.16 \times {10^6}{m^{ - 1}}. The other properties of waves and sine waves, such as their frequency, amplitude, phase, and speed.