Wavenumber of an electromagnetic radiation

1. Wave number of an electromagnetic radiation

2. What is the wavenumber of an electromagnetic radiation?  The wavenumber of light radiation is the number of waves per meter.  And it is reciprocal to the wavelength of the electromagnetic radiation.  The Greek symbol Ῡ (nu bar) denotes it.  And it is expressed as m-1 in SI units.

3. What is the relationship between the wavenumber and wavelength?  The wavenumber of an electromagnetic wave varies inversely with its wavelength.  Irrespective of the name, the wavenumber & wavelength suggests the energy associated with the light radiation.  Besides, the wavenumber and wavelength are inversely proportional to each other.  It implies electromagnetic radiations with shorter wavelengths have higher wavenumbers. Similarly, longer wavelength radiations have shorter wavenumbers. Energy of light Wavenumber Wavelength

4. Why do electromagnetic waves with high energy have higher values of wavenumber?  According to the quantum theory, the wavenumber of an electromagnetic Increase radiation varies directly with the photon energy. Wave Photon Increase  Hence, the electromagnetic waves with number energy high energy have higher values of wavenumber. Conversely, low wavenumber suggests less energetic waves

5. What is the relationship between the wavenumber and photon energy in quantum theory?  The quantum theory of radiation states that each quantum is associated with a definite amount of energy depending upon the wavenumber of radiation. Hence, the photon's energy is directly proportional to its wavenumber. Energy- Frequency Frequency formula Wavenumber formula Formula derivation

6. Numerical problem-1 Question: Calculate the wavenumber and wavelength of the spectral line when the electron in a hydrogen atom undergoes a transition from n=4 to n=2? Answer: The hydrogen electron transition principal quantum state details are n1=2 and n2=4. The formula to calculate the wavelength of the spectral line is below; Where, R is the Rydberg constant

7. By substituting the values of R, n1and n2, we get the wavenumber of the spectral line. 1 λ= ? 1 1 2?−1 2− ?1 ?2 1 λ= 10.97 × 106 1 22− 1 42?−1 1 λ= ???? ?????? (Ῡ) = 2.056 × 106?−1 1 2.056 × 106?−1= 0.486 × 10−6? = 486 ?? ???? ?????ℎ = λ = Hence, the wavenumber of the spectral line is 2.056X106m-1and the wavelength of the spectral line is 486 nm

8. Numerical problem-2 Question: Calculate the wavenumber of yellow radiation having wavelength 5800 A0 Answer: The wavelength of yellow radiation is 5800 A0, it’s wavenumber can be calculated by the following formula; Wavenumber calculation is below; Ῡ =1 1 5800 × 10−10?= 1.724 × 106?−1 λ= Where, R is the Rydberg constant

9. Numerical problem-3 Question: Calculate the wavenumber for the shortest wavelength transition in the Balmer series of the hydrogen spectrum? The shortest wavelength of the Balmer series involves the electron transition from n1=2 to n2=∞. The formula to calculate it’s wavenumber is here;

10. By substituting the values of R, n1and n2in the above equation, we get; 1 22− 1 Ῡ = 10.97 × 106 ∞2?−1 Ῡ =10.97 × 106 ?−1 4 Ῡ = 2.7425 × 106?−1 So, the wavenumber for the shortest wavelength in the Balmer series of the hydrogen spectrum is equal to 2.7425X106m-1

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