Chapter 26, Problem 34QAP

To determine

The spreadsheet for 15 values of$\frac{\Delta I}{\Delta \lambda }$and use graph of it to compare 3 values of temperature.

Explanation of Solution

Given:

Plank's constant,$h=6.63\times {10}^{-34}\text{Js}$.

Speed of light,$c=3\times {10}^8\text{m/s}$.

Boltzmann's constant,$k=1.38\times {10}^{-23}\text{J/K}$.

Formula used:

$\frac{\Delta I}{\Delta \lambda }=\frac{2\pi h{c}^2}{{\lambda }^5}\left(\frac{1}{e^{\raisebox{1ex}{$hc$}\!\left/ \!\raisebox{-1ex}{$\lambda k_{B}T$}\right.}-1}\right)$.

The intensity of light emitted per wavelength range is,

$\frac{\Delta I}{\Delta \lambda }=\frac{2\pi h{c}^2}{{\lambda }^5}\left(\frac{1}{e^{\raisebox{1ex}{$hc$}\!\left/ \!\raisebox{-1ex}{$\lambda k_{B}T$}\right.}-1}\right)$.

For temperature,T=100K.

Number of observations	Wavelength ($\text{μm}$ )	$\frac{\Delta I}{\Delta \lambda }$
1	0	0
2	0.5	$41.59\times {10}^6$
3	1	$2.59\times {10}^6$
4	1.5	$5.13\times {10}^5$
5	2	$1.62\times {10}^5$
6	2.5	$6.65\times {10}^5$
7	3	$3.20\times {10}^4$
8	3.5	$1.73\times {10}^4$
9	4	$1.015\times {10}^4$
10	4.5	$1.142\times {10}^4$
11	5	$4.159\times {10}^3$
12	5.5	$2.839\times {10}^3$
13	6	2002.35
14	6.5	2164.7
15	7	1025

.

For temperature,T=200K.

Number of observations	Wavelength ($\text{μm}$ )	$\frac{\Delta I}{\Delta \lambda }$
1	0	0
2	0.5	$83.19\times {10}^6$
3	1	$5.19\times {10}^6$
4	1.5	$1.026\times {10}^6$
5	2	$3.24\times {10}^5$
6	2.5	$1.33\times {10}^5$
7	3	$6.41\times {10}^4$
8	3.5	$3.462\times {10}^4$
9	4	$2.031\times {10}^4$
10	4.5	$1.267\times {10}^4$
11	5	$9.151\times {10}^3$
12	5.5	5451.2
13	6	4012.2
14	6.5	2904.32
15	7	2156.38

.

The plot of the set of data. The different colors of lines in the graph implies the plot for different temperature..

Conclusion:

The curves changes as the temperature changes. The different lines in the plot shows the plots for different temperature.