The energy emitted by a black body's surface per unit area at a particul ar wavelength can be calcul ated using Planck's Radiation Law, which can be written as follows, 2nhc? E(2, T') = 25. (ehc/AkT -1) where his Planck's constant 6.626 x 10-27 erg s, cis the speed oflight, kis the Boltzmann constant = 1.38 x 10-18 erg/K, Tis the temperature in Kelvins and A is the wavelength in um. If E is given in erg/um, what are the units of the constant 2n, given that the equation is valid and therefore dimensionall y homogenous? If the speed of light is 3.00x10% m/s, what value and unit should be used for c in this equation to maintain dimensional homogeneity? Note: erg is a unit of energy equal to 10-7 Joules and the whole expression (ehc/akT – 1) ends up dimensionless.
The energy emitted by a black body's surface per unit area at a particul ar wavelength can be calcul ated using Planck's Radiation Law, which can be written as follows, 2nhc? E(2, T') = 25. (ehc/AkT -1) where his Planck's constant 6.626 x 10-27 erg s, cis the speed oflight, kis the Boltzmann constant = 1.38 x 10-18 erg/K, Tis the temperature in Kelvins and A is the wavelength in um. If E is given in erg/um, what are the units of the constant 2n, given that the equation is valid and therefore dimensionall y homogenous? If the speed of light is 3.00x10% m/s, what value and unit should be used for c in this equation to maintain dimensional homogeneity? Note: erg is a unit of energy equal to 10-7 Joules and the whole expression (ehc/akT – 1) ends up dimensionless.
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Transcribed Image Text:The energy emitted by a black body's surface per unit area at a particul ar wavelength can
be calcul ated using Planck's Radiation Law, which can be written as follows,
2nhc?
E(2, T) =
25. (ehc/kT -1)
where his Planck's constant 6.626 x 10-27 erg.s, c is the speed oflight, kis the Boltzmann
constant = 1.38 x 10-18 erg/K, Tis the temperature in Kelvins and A is the wavelength in
um.
If E is given in erg/um?, what are the units of the constant 2n, given that the equation is
valid and therefore dimensionally homogenous? If the speed of light is 3.00x10$ m/s, what
value and unit should be used for c in this equation to maintain dimensional homogeneity?
Note: erg is a unit of energy equal to 10-7 Joules and the whole expression
(ehc/AkT – 1) ends up dimensionless.
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