Respuesta :
Answer:
The number of photons per second are [tex]7.95\times10^{11}\ photons/s[/tex].
Explanation:
Given that,
Wavelength = 650 nm
Power = 45 W
Distance R= 17 m
Diameter = 5.0 mm
We need to calculate the number of photon per second emitted by light bulb
Using formula of energy
[tex]E=\dfrac{hc}{\lambda}[/tex]
The power is
[tex]P=\dfrac{nE}{t}[/tex]
[tex]\dfrac{n}{t}=\dfrac{P}{E}[/tex]
Put the value of E
[tex]\dfrac{n}{t}=\dfrc{P \lambda}{hc}[/tex]
Put the value into the formula
[tex]\dfrac{n}{t}=\dfrac{45\times650\times10^{-9}}{6.6\times10^{-34}\times3\times10^{8}}[/tex]
[tex]\dfrac{n}{t}=1.47\times10^{20}\ photons/s[/tex]
We need to calculate the surface area
Using formula of area
[tex]A=4\piR^2[/tex]
[tex]A=4\pi\times17^2[/tex]
We need to calculate the number of photons entering into eye
[tex]N=n\dfrac{A_{eye}}{A_{surface}}[/tex]
[tex]N=1.47\times10^{20}\times\dfrac{\pi(2.5\times10^{-3})^2}{4\pi\times17^2}[/tex]
[tex]N=7.95\times10^{11}\ photons/s[/tex]
Hence, The number of photons per second are [tex]7.95\times10^{11}\ photons/s[/tex].
A. 1.5 × 10²⁰ photons per second are emitted by a monochromatic lightbulb
B. 8.0 × 10¹¹ photons per second enter each of the eyes
[tex]\texttt{ }[/tex]
Further explanation
The term of package of electromagnetic wave radiation energy was first introduced by Max Planck. He termed it with photons with the magnitude is :
[tex]\large {\boxed {E = h \times f}}[/tex]
E = Energi of A Photon ( Joule )
h = Planck's Constant ( 6.63 × 10⁻³⁴ Js )
f = Frequency of Eletromagnetic Wave ( Hz )
[tex]\texttt{ }[/tex]
The photoelectric effect is an effect in which electrons are released from the metal surface when illuminated by electromagnetic waves with large enough of radiation energy.
[tex]\large {\boxed {E = \frac{1}{2}mv^2 + \Phi}}[/tex]
[tex]\large {\boxed {E = qV + \Phi}}[/tex]
E = Energi of A Photon ( Joule )
m = Mass of an Electron ( kg )
v = Electron Release Speed ( m/s )
Ф = Work Function of Metal ( Joule )
q = Charge of an Electron ( Coulomb )
V = Stopping Potential ( Volt )
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
Given:
wavelength of the light = λ = 650 nm = 6.5 × 10⁻⁷ m
power of lightbulb = P = 45 W
distance between the eyes and the bulb = R = 17 m
diameter of pupil = d = 5.0 mm = 5.0 × 10⁻³ m
Asked:
A. total number of photons per second = N/t = ?
B. number of photon per second entering the eyes = n/t = ?
Solution:
Part A:
[tex]P = E \div t[/tex]
[tex]P = N h f \div t[/tex]
[tex]P = \frac{N}{t} hf[/tex]
[tex]\frac{N}{t} = P \div (hf}[/tex]
[tex]\frac{N}{t} = P \div (h\frac{c}{\lambda})[/tex]
[tex]\frac{N}{t} = 45 \div (6.63 \times 10^{-34} \times \frac{3 \times 10^8}{6.5 \times 10^{-7}})[/tex]
[tex]\boxed{\frac{N}{t} \approx 1.5 \times 10^{20} \texttt{ photons/second}}[/tex]
[tex]\texttt{ }[/tex]
Part B:
[tex]\frac{n}{t} = \frac{A_{eye}}{A_{total}} \times \frac{N}{t}[/tex]
[tex]\frac{n}{t} = \frac{\frac{1}{4} \pi d^2}{4 \pi R^2} \times \frac{N}{t}[/tex]
[tex]\frac{n}{t} = \frac{d^2}{16 R^2} \times \frac{N}{t}[/tex]
[tex]\frac{n}{t} = \frac{(5.0 \times 10^{-3})^2}{16 \times 17^2} \times 1.5 \times 10^{20}[/tex]
[tex]\boxed{\frac{n}{t} = 8.0 \times 10^{11} \texttt{ photons/second} }[/tex]
[tex]\texttt{ }[/tex]
Learn more
- Photoelectric Effect : https://brainly.com/question/1408276
- Statements about the Photoelectric Effect : https://brainly.com/question/9260704
- Rutherford model and Photoelecric Effect : https://brainly.com/question/1458544
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Answer details
Grade: College
Subject: Physics
Chapter: Quantum Physics
