Question

Nitrogen laser produces radiation at a wavelength of 337.1nm. if the number of photons emitted is $5.6\times {{10}^{24}}$ . Calculate the power of this laser.

Answer 1

Hint: Results observed that the interactions of radiations with the matter have provided more information regarding the structure of atoms and molecules. From these results, Neils Bohr improved a model which is proposed by Rutherford. Two major developments by Bohr’s model of an atom.

Complete step by step solution:
Two important developments played a major role in the formation of Bohr’s model of an atom. These are:
(i) Dual character of electromagnetic radiation
Different types are used to represent electromagnetic radiation. These radiations are characterized by the properties of wavelength and frequency. Various types of electromagnetic radiations will differ from their wavelength and frequency.
Especially in spectroscopy, a commonly used quantity is the wavenumber. This is defined as the number of wavelengths per unit length. Its unit is the reciprocal of the wavelength unit $c{{m}^{-1}}$ . Small waves of different kinds in electromagnetic radiation have smaller wavelengths and smaller units.
(ii) Experimental results of atomic spectra
If electrons have quantized energy levels only, these experimental results will explain.
According to Planck’s quantum theory,
 The power of laser is, $E=\dfrac{Nhc}{\lambda }$ -- (1)
Where, E = power of laser
N = no of photons = $5.6\times {{10}^{24}}$
h = Planck’s constant = $6.625\times {{10}^{-34}}Js$
c = speed of light = $3\times {{10}^{8}}m/\sec $
$\lambda $ = 337.1nm
Substitute the above value in the equation (1)
$E=\dfrac{5.6\times {{10}^{24}}\times 6.62\times {{10}^{-24}}\times 3\times {{10}^{8}}}{337.1\times {{10}^{-19}}}=3.3\times {{10}^{6}}J/s$

Hence, the power of the nitrogen laser at 337.1 nm = $3.3\times {{10}^{6}}W$

Note: An ultraviolet range operating gas laser is a nitrogen laser, which is molecular nitrogen as a medium pumped in an electrical discharge. This nitrogen laser is three-level lasers. The wavelength of the nitrogen laser in the ultraviolet at 337.1nm