5.10 pts. a. Starting from expression in notes M(v,T) where v = 1/λ . for Ma(X,T) [Watt/m³], develop an expression for b. What are the units of M, (v,T) in your expression? • Planck equation can be expressed in other variables than wavelength, such as frequency (f) or wavenumber (ỹ). • Use the relations λ f= c and v=1/λ to convert the equations BUT BE CAREFUL to convert the differential also. • Start out with in-band quantities on both sides of the equations (like W/cm²). • For instance, to convert from M, (2,7) in [Watt/(cm² µm)] λ to M, (f,T) in [Watt/(cm² Hz)], begin with: M (2,T) d = M, (ƒ,T) df λ f • Units of both sides are W/cm² (after factor of ten conversion). • From λ f = c, by derivative, |d2|=|df| f 2πhc² λ M₁ (λ,T) dλ= 25 2 [ec hc/2kT - So M, (f,T) = 3. 2лhƒ³ C² [ef KT - 1] of ten conversion). -dλ = 5 2лhc² hf/kT A Lever-1] |df|- [Watt/(cm² Hz)], (after factor
5.10 pts. a. Starting from expression in notes M(v,T) where v = 1/λ . for Ma(X,T) [Watt/m³], develop an expression for b. What are the units of M, (v,T) in your expression? • Planck equation can be expressed in other variables than wavelength, such as frequency (f) or wavenumber (ỹ). • Use the relations λ f= c and v=1/λ to convert the equations BUT BE CAREFUL to convert the differential also. • Start out with in-band quantities on both sides of the equations (like W/cm²). • For instance, to convert from M, (2,7) in [Watt/(cm² µm)] λ to M, (f,T) in [Watt/(cm² Hz)], begin with: M (2,T) d = M, (ƒ,T) df λ f • Units of both sides are W/cm² (after factor of ten conversion). • From λ f = c, by derivative, |d2|=|df| f 2πhc² λ M₁ (λ,T) dλ= 25 2 [ec hc/2kT - So M, (f,T) = 3. 2лhƒ³ C² [ef KT - 1] of ten conversion). -dλ = 5 2лhc² hf/kT A Lever-1] |df|- [Watt/(cm² Hz)], (after factor
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Could you please help me with number 5. I was told everything to do the problem is on the set of notes I attached. I would re
![5.10 pts.
a. Starting from expression in notes
M(v,T) where v = 1/λ .
for Ma(X,T) [Watt/m³], develop an expression for
b. What are the units of M, (v,T) in your expression?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc158a850-76a9-4504-97b9-8593e0926539%2Fa777dcd5-a2e4-40dd-95b2-e9b40caabe7d%2Fhjfciz4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.10 pts.
a. Starting from expression in notes
M(v,T) where v = 1/λ .
for Ma(X,T) [Watt/m³], develop an expression for
b. What are the units of M, (v,T) in your expression?
![• Planck equation can be expressed in other variables than
wavelength, such as frequency (f) or wavenumber (ỹ).
• Use the relations λ f= c and v=1/λ to convert the equations
BUT BE CAREFUL to convert the differential also.
• Start out with in-band quantities on both sides of the
equations (like W/cm²).
• For instance, to convert from M, (2,7) in [Watt/(cm² µm)]
λ
to M, (f,T) in [Watt/(cm² Hz)], begin with:
M (2,T) d = M, (ƒ,T) df
λ
f
• Units of both sides are W/cm² (after factor of ten
conversion).
• From λ f = c, by derivative, |d2|=|df|
f
2πhc²
λ
M₁ (λ,T) dλ=
25
2 [ec
hc/2kT
-
So M, (f,T)
=
3.
2лhƒ³
C² [ef KT - 1]
of ten conversion).
-dλ =
5
2лhc²
hf/kT
A Lever-1]
|df|-
[Watt/(cm² Hz)], (after factor](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc158a850-76a9-4504-97b9-8593e0926539%2Fa777dcd5-a2e4-40dd-95b2-e9b40caabe7d%2Flckl42h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:• Planck equation can be expressed in other variables than
wavelength, such as frequency (f) or wavenumber (ỹ).
• Use the relations λ f= c and v=1/λ to convert the equations
BUT BE CAREFUL to convert the differential also.
• Start out with in-band quantities on both sides of the
equations (like W/cm²).
• For instance, to convert from M, (2,7) in [Watt/(cm² µm)]
λ
to M, (f,T) in [Watt/(cm² Hz)], begin with:
M (2,T) d = M, (ƒ,T) df
λ
f
• Units of both sides are W/cm² (after factor of ten
conversion).
• From λ f = c, by derivative, |d2|=|df|
f
2πhc²
λ
M₁ (λ,T) dλ=
25
2 [ec
hc/2kT
-
So M, (f,T)
=
3.
2лhƒ³
C² [ef KT - 1]
of ten conversion).
-dλ =
5
2лhc²
hf/kT
A Lever-1]
|df|-
[Watt/(cm² Hz)], (after factor
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