Compute the energy and momentum of a single photon of visible light for wavelengths of 4000 a, 6000 a, and 8000 a, where 1 10-10 meter. repeat for an infrared photon of 1,000,000 a and an ultra- violet photon of 500 a. comment on the results.

Explanation:

To calculate the energy we will use the Planck equation and to calculate the moment we will use the Brolle equation

               E = h f

               P = h / λ

With the constant that is worth 6.63 10-34 J s

Wavelengths are λ= 4000 A = 4000 10-10 = 4 10-7 m

The speed of light is the product of the frequency by the wavelength of the radiation

           c = λ f

           f = c / λ

           f = 3 10⁸/4 10⁻⁷

           f = 7.5 10¹⁴ Hz

          E = 6.63 10⁻³⁴ /7.5 10¹⁴

          E = 49.7 10⁻⁴⁸ J

          P = 6.63 10⁻³⁴ / 4 10⁻⁷

          P = 1.66 10⁻²⁷

          λ = 6000 A = 6 10⁻⁷ m

          f = 3 108/5 10-7 = 5 10¹⁴ Hz

          E = 6.63 10⁻³⁴ / 5 10¹⁴ = 1.3 10⁻⁴⁸ Hz

          P = 6.63 10⁻³⁴ / 6 10⁻⁷ = 1.1 10⁻²⁷

          λ = 8000 a = 8 10⁻⁷

          f = 3 10⁸/8 10⁻⁷ = 3.75 10¹⁴ Hz

          E = 6.63 10⁻³⁴ / 3.75 10¹⁴ = 1.77 10⁻⁴⁸ Hz

          P = 6.63 10⁻³⁴ / 8 10⁻⁷ = 8.2 10⁻²⁷

          λ = 1000000 = 1 10⁻⁴ m

          f = 3 10⁸/1 10⁻⁴ = 3 10¹² Hz  

          E = 6.63 10⁻³⁴ / 3 10¹² = 2.21 10⁻⁴⁶ Hz

          P = 6.63 10⁻³⁴ / 8 10⁻⁷ = 8.2 10⁻²⁷

          λ = 500 A = 5 10⁻⁸ m

          f = 3 10⁸/5 10⁻⁸ = 6 10¹⁵ Hz

          E = 6.63 10⁻³⁴ / 5 10¹⁵ = 1.33 10⁻⁴⁹ Hz

          P = 6.63 10⁻³⁴ / 5 10⁻⁸ = 1.33 10⁻²⁶ Kg m / s²

We see that the energy of the ultraviolet photon is much greater (two orders of magnitude) than that of the infrared photon

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