Question

Power emitted per unit area of a black body is R " watt/m"^(2). At what wavelength will the power radiated by black body be maximum is stefan's constant is sigma and Wien's constant is b then.

Answer 1

Given: Power emitted per unit area of a black body is R  watt/m²

To find: wavelength = ?

Solution:

• Now we have given that power emitted per unit area is R, also stefans constant is given as sigma.
• We know that, power emitted is directly proportional to the fourth power of T, so:

                 R ∝ T^4

• After removing the proportionality, we have to add a constant.
• So the constant is sigma.

                 R = (sigma) T^4

• As we know, according to Wein's theorem, maximum of wavelength and T is equal to b, so

                 lambda x T = b

                 calculating further we get:

                 (lambda) max = B/T

• From above equation, put value of T in lambda, we get:

                 (lambda) max = B / (R / sigma)^1/4

                 (lambda) max = B x (sigma / R)^1/4

Answer:

              Wavelength is  B x (sigma / R)^1/4

Answer 2

All objects emit electromagnetic radiation according to their temperature. A black body is an idealized object that absorbs all electromagnetic radiation