Respuesta :
Answer:
a) E₀ = 2.125 eV, b) # photon2 = 9.2 10¹⁵ photons / mm²
Explanation:
a) To calculate the energy of a photon we use Planck's education
E = h f
And the ratio of the speed of light
c = λ f
We replace
E = h c /λ
Let's calculate
E₀ = 6.63 10⁻³⁴ 3 10⁸/585 10⁻⁹
E₀ = 3.40 10⁻¹⁹ J
Let's reduce
E₀ = 3.4 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)
E₀ = 2.125 eV
b) Let's look for the energy in each pulse
P = E / t
E = P t
E = 20.0 0.45 10⁻³
E = 9 10⁻³ J
let's use a ratio of proportions (rule of three) if we have the energy of a photon (E₀), to have the energy of 9 10⁻³ J
# photon = 9 10⁻³ /3.40 10⁻¹⁹
# photon = 2.65 10¹⁶ photons
Let's calculate the areas
Focus area
A₁ = π r²
A₁ = π (3.4/2)²
A₁ = 9,079 mm²2
Area requested for calculation r = 1 mm
A₂ = π 1²
A₂ = 3.1459 mm²
Let's use another rule of three. If we have 2.65 106 photons in an area A1 how many photons in an area A2
# photon2 = 2.65 10¹⁶ 3.1459 / 9.079
# photon2 = 9.2 10¹⁵ photons / mm²
The energy of each photon is 2.12eV and the number of photons per square millimeter is 2.92*10^15 photons/mm^2
Data;
- Wavelength = 585nm
- Energy = ?
- speed of light (c) = 3.0*10^8 m/s
- Planks constant (h) = 6.626*10^-34 JS
Energy of each Photon
The energy of each photon can be calculated as
[tex]E = \frac{hc}{\lambda} \\E = \frac{6.626*10^-^3^4 * 3.0*10^8}{585*10^-^9} \\E = 3.39*10^-^1^9J\\E = \frac{3.39*10^-^1^9}{1.60*10^-^1^9} \\E = 2.12eV[/tex]
The energy of each photon is 2.12eV
Number of Photons per square millimeter
power = 20w
diameter = 3.4mm
Number of photons
[tex]n = \frac{power}{energy} * 0.45\\n = \frac{20}{3.39*10^-^1^9} * 0.45*10^-^3 = 2.65*10^1^6 photons[/tex]
The number of photons per square millimeter is
[tex]N'=\frac{2.65*10^1^6}{\pi (d/2)^2} \\N' = 2.92*10^1^5 photons/mm^2[/tex]
The number of photons per square millimeter is 2.92*10^15 photons/mm^2
Learn more on energy of a photon here;
https://brainly.com/question/7464909
