Question

1a

Demonstrate how the spectral emissive power inside a blackbody cavity changes with respect to the
following parameters:
a) Temperature and wavelength, hence, find E?(?, T), by:
(i) Creating a table with the (?, T) values as follows:
1. Wavelengths, ?, from 0.1 ?m to 100 ?m, on the first (left-most) column. Use increments
of:
? 0.1 ?m from 0.1 ?m to 1.0 ?m;
? 0.5 ?m from 1.0 ?m to 10 ?m;
? 1.0 ?m from 10 ?m to 100 ?m;
2. Temperatures, T, values of: 273.15 K; 773.15 K; 1273.15 K; 1773.15 K; 2273.15 K; 5000
K; and, 10000 K.
3. Calculate E?(?, T) using units of W/m2·?m and assume the constants C1 = 374210000
and C2 = 14388.
Set up your table with each separate column corresponding to each given value of T.
Ensure that you clearly label each column in your table and include the relevant units.
[Hint: There should be seven separate columns in your table for the E?(?, T) calculations
and eight columns in your table altogether with the inclusion of the left-most column
consisting of the ? values.
The recommendation is that you fill in each separate column in your table using a
different background colour in order to facilitate the examination of the different T
calculations and to assist in identifying the corresponding plots.]
4. Clearly demarcate the visible region in your table. You may do this by selecting a
different coloured font for the values of ? (and the corresponding E? values) that fall
within this region.
(ii) Plot the calculated values of E?(?, T) ensuring that you set out each plot as follows:
1. Display the calculated E?(?, T) values on the vertical axis.
2. Display the wavelengths on the horizontal axis. Select the logarithmic scale, to base 10,
to display your values on this axis.
3. Clearly demarcate the visible region in each plot.
4. Include a title in each plot, clearly identifying the relevant value of T and ensure that you
label both axes (including units).
[Hint: The recommendation is that you fill in the background of each plot in the same
colour as the corresponding column in your table in order to facilitate the analyses of
the different T calculations.]

Planck's Law may be encountered in a number of different forms depending on the conventions and
preferences of different scientific fields

b) Set up a table in an Excel Worksheet providing the following information:
(i) Variables:
1. Frequency
2. Wavelength
3. Wavenumber
4. Angular Frequency
5. Angular Wavelength
6. Angular Wavenumber
(ii) Symbols for the Variables
(iii) The formula for Planck's Law expressed in terms of each different spectral variable.
(iv) Whether the formula is most often encountered in experimental fields or theoretical fields.
c) Calculate the following:
(i) An electromagnetic wave has a wavelength of 550 nm.
1. What is the frequency of radiation of this wave?
2. Can humans perceive this wave? If so, how do we perceive it? If not, what form of
radiation is this wave in relation to the electromagnetic spectrum?
(ii) During a night out on the town we see many different lighted signs at the late-night diners.
One particular sign catches our attention, if the radiation from the excited atoms which
produce the light in this sign have a wavelength of 680 nm, what is the energy of each
photon that is being emitted by this sign?
(iii) Given that the energy of the photons being emitted from a particular metal is 6.54×10–19J,
what is the frequency and wavelength of this radiation?

Answer 1