Consider the Planck function in both its frequency and wavelength forms:
a) For the Planck function, B_(v)(T), what is the most probable frequency v_(p) at a given
temperature? [Hint: derive one or more expressions by differentiating the Planck function and
considering the limits of zero and infinity for the frequency. There is no need to derive values.]
b) For the Planck function expressed as a function of wavelength, B_(lambda )(T), what is the most
probable wavelength lambda _(p) at a given temperature?
c) Are v_(p) and lambda _(p) consistent with the relationship v=(c)/(lambda ) ? Explain your answer.
d) For what range of temperature does lambda _(p) fall in the visible range of the electromagnetic
spectrum? How does this compare with the effective temperature of the Sun?
Consider the Planck function in both its freguency and wavelength forms:
a) For the Planck function, B,(T), what is the most probable frequency Up at a given
temperature?[Hint:derive one or more expressions by differentiating the Planck function and
considering the limits of zero and infinity for the frequency.There is no need to derive values.]
b)For the Planck function expressed as a function of wavelength,B(),what is the most
probable wavelength Ap at a given temperature?
c) Are U, and p consistent with the relationship u = c/? Explain your answer.
d) For what range of temperature does p fall in the visible range of the electromagnetic
spectrum? How does this compare with the effective temperature of the Sun?