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

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =