Spectral Radiant Emittance Calculator

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Photonics Devices

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✖Wavelength of Visible Light is the band of wavelengths in the range 400nm - 800nm of the electromagnetic spectrum that is visible to the human eye.ⓘ Wavelength of Visible Light [λ_vis]			+10% -10%
✖Absolute Temperature represents the temperature of the system.ⓘ Absolute Temperature [T]			+10% -10%

✖Spectral Radiant Emittance is the power radiated from a blackbody per unit area and is given by W.ⓘ Spectral Radiant Emittance [W_sre]

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Formula

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Spectral Radiant Emittance

Formula

`"W"_{"sre"} = (2*pi*"[hP]"*"[c]"^3)/"λ"_{"vis"}^5*1/(exp(("[hP]"*"[c]")/("λ"_{"vis"}*"[BoltZ]"*"T"))-1)`

Example

`"5.7E^-8W/(m²*Hz)"=(2*pi*"[hP]"*"[c]"^3)/("500nm")^5*1/(exp(("[hP]"*"[c]")/("500nm"*"[BoltZ]"*"393K"))-1)`

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Spectral Radiant Emittance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spectral Radiant Emittance = (2*pi*[hP]*[c]^3)/Wavelength of Visible Light^5*1/(exp(([hP]*[c])/(Wavelength of Visible Light*[BoltZ]*Absolute Temperature))-1)
W_sre = (2*pi*[hP]*[c]^3)/λ_vis^5*1/(exp(([hP]*[c])/(λ_vis*[BoltZ]*T))-1)
This formula uses 4 Constants, 1 Functions, 3 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
[hP] - Planck constant Value Taken As 6.626070040E-34
[c] - Light speed in vacuum Value Taken As 299792458.0
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Spectral Radiant Emittance - (Measured in Watt per Square Meter per Hertz) - Spectral Radiant Emittance is the power radiated from a blackbody per unit area and is given by W.
Wavelength of Visible Light - (Measured in Meter) - Wavelength of Visible Light is the band of wavelengths in the range 400nm - 800nm of the electromagnetic spectrum that is visible to the human eye.
Absolute Temperature - (Measured in Kelvin) - Absolute Temperature represents the temperature of the system.

STEP 1: Convert Input(s) to Base Unit

Wavelength of Visible Light: 500 Nanometer --> 5E-07 Meter (Check conversion here)
Absolute Temperature: 393 Kelvin --> 393 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_sre = (2*pi*[hP]*[c]^3)/λ_vis^5*1/(exp(([hP]*[c])/(λ_vis*[BoltZ]*T))-1) --> (2*pi*[hP]*[c]^3)/5E-07^5*1/(exp(([hP]*[c])/(5E-07*[BoltZ]*393))-1)

Evaluating ... ...

W_sre = 5.70045847765288E-08

STEP 3: Convert Result to Output's Unit

5.70045847765288E-08 Watt per Square Meter per Hertz --> No Conversion Required

FINAL ANSWER

5.70045847765288E-08 ≈ 5.7E-8 Watt per Square Meter per Hertz <-- Spectral Radiant Emittance

(Calculation completed in 00.004 seconds)

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Created by Priyanka G Chalikar

The National Institute Of Engineering (NIE), Mysuru

Priyanka G Chalikar has created this Calculator and 10+ more calculators!

Verified by Parminder Singh

Chandigarh University (CU), Punjab

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< 13 Photonics Devices Calculators

Saturation Current Density

Go Saturation Current Density = [Charge-e]*((Diffusion Coefficient of Hole)/Diffusion Length of Hole*Hole Concentration in n-Region+(Electron Diffusion Coefficient)/Diffusion Length of Electron*Electron Concentration in p-Region)

Spectral Radiant Emittance

Go Spectral Radiant Emittance = (2*pi*[hP]*[c]^3)/Wavelength of Visible Light^5*1/(exp(([hP]*[c])/(Wavelength of Visible Light*[BoltZ]*Absolute Temperature))-1)

Contact Potential Difference

Go Voltage Across PN Junction = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Carrier Concentration)^2)

Energy Density given Einstein Co-Efficients

Go Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1))

Proton Concentration under Unbalanced Condition

Go Proton Concentration = Intrinsic Electron Concentration*exp((Intrinsic Energy Level of Semiconductor-Quasi Fermi Level of Electrons)/([BoltZ]*Absolute Temperature))

Total Current Density

Go Total Current Density = Saturation Current Density*(exp(([Charge-e]*Voltage Across PN Junction)/([BoltZ]*Absolute Temperature))-1)

Net Phase Shift

Go Net Phase Shift = pi/Wavelength of Light*(Refractive Index)^3*Length of Fiber*Supply Voltage

Relative Population

Go Relative Population = exp(-([hP]*Relative Frequency)/([BoltZ]*Absolute Temperature))

Optical Power Radiated

Go Optical Power Radiated = Emissivity*[Stefan-BoltZ]*Area of Source*Temperature^4

Mode Number

Go Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength

Wavelength of Radiation in Vaccum

Go Wavelength of Wave = Apex Angle*(180/pi)*2*Single Pinhole

Wavelength of Output Light

Go Wavelength of Light = Refractive Index*Photon Wavelength

Length of Cavity

Go Length of Cavity = (Photon Wavelength*Mode Number)/2

Spectral Radiant Emittance Formula

What is the significance of this equation?

During the derivation of spectral radiant emittance, Planck assumed that matter could only emit discrete quantities of radiation which were called photons. The success of this assumption, provided for the foundation of modern quantum theory.

How to Calculate Spectral Radiant Emittance?

Spectral Radiant Emittance calculator uses Spectral Radiant Emittance = (2*pi*[hP]*[c]^3)/Wavelength of Visible Light^5*1/(exp(([hP]*[c])/(Wavelength of Visible Light*[BoltZ]*Absolute Temperature))-1) to calculate the Spectral Radiant Emittance, The Spectral Radiant Emittance formula is defined as the power radiated by the by the back body per unit area. Emittance is also known as Exitance. Spectral Radiant Emittance is denoted by W_sre symbol.

How to calculate Spectral Radiant Emittance using this online calculator? To use this online calculator for Spectral Radiant Emittance, enter Wavelength of Visible Light (λ_vis) & Absolute Temperature (T) and hit the calculate button. Here is how the Spectral Radiant Emittance calculation can be explained with given input values -> 5.7E-8 = (2*pi*[hP]*[c]^3)/5E-07^5*1/(exp(([hP]*[c])/(5E-07*[BoltZ]*393))-1).

FAQ

What is Spectral Radiant Emittance?

The Spectral Radiant Emittance formula is defined as the power radiated by the by the back body per unit area. Emittance is also known as Exitance and is represented as W_sre = (2*pi*[hP]*[c]^3)/λ_vis^5*1/(exp(([hP]*[c])/(λ_vis*[BoltZ]*T))-1) or Spectral Radiant Emittance = (2*pi*[hP]*[c]^3)/Wavelength of Visible Light^5*1/(exp(([hP]*[c])/(Wavelength of Visible Light*[BoltZ]*Absolute Temperature))-1). Wavelength of Visible Light is the band of wavelengths in the range 400nm - 800nm of the electromagnetic spectrum that is visible to the human eye & Absolute Temperature represents the temperature of the system.

How to calculate Spectral Radiant Emittance?

The Spectral Radiant Emittance formula is defined as the power radiated by the by the back body per unit area. Emittance is also known as Exitance is calculated using Spectral Radiant Emittance = (2*pi*[hP]*[c]^3)/Wavelength of Visible Light^5*1/(exp(([hP]*[c])/(Wavelength of Visible Light*[BoltZ]*Absolute Temperature))-1). To calculate Spectral Radiant Emittance, you need Wavelength of Visible Light (λ_vis) & Absolute Temperature (T). With our tool, you need to enter the respective value for Wavelength of Visible Light & Absolute Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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