Blackbodies - Wien's Law and Planck's Radiation Formula

[lachy]

Homework Statement

I have been given Planck's Radiation law and Wien's Law, and need to say whether the values produced from both are the same or different.

Homework Equations

Planck's Equation:

Wien's Law:

The Attempt at a Solution

So, I have completed the task of inserting data and graphing it but cannot figure it out. Here is what I have done so far but I cannot figure out the reasons why the values and graphs would be slightly different. The Planck wavelength values are from another spreadsheet which have been generated using Planck's radiation formula:

I would appreciated your help :)

-Lachlan

 

[ehild]

It is all right within 1 significant digits. Can not you read lambda(max) with a bit higher accuracy? It would be better to write out the data with 2 significant digits in normal form without that lot of zeros.

ehild

 

[lachy]

Thank you for replying :)
Yes but they are two formulae that show the same thing - surely there should not be any anomalies with the data if it is all consistent? What I mean is, it shouldn't matter how many significant figures - it should all work out shouldn't it?

 

[ehild]

Yes, but your lambda(max) values obtained from Planck's law are very inaccurate. If you determine them with 2 significant digits, the values will be closer.

ehild

 

[vela]

Thank you for replying :)
Yes but they are two formulae that show the same thing - surely there should not be any anomalies with the data if it is all consistent? What I mean is, it shouldn't matter how many significant figures - it should all work out shouldn't it?

Whenever you compare two numbers, practically speaking, the number of significant figures is crucial in determining whether they are equal or not. After all, that's the whole point of significant figures, isn't it?

The constant you have in Wien's law has only two sig figs, so your answers are only good to two sig figs. The constants for Planck's equation have four sig figs, so your answers from it are good to four sig figs. When you compare the results, you're limited by the least precise numbers, so you should round all the figures to two significant figures and then compare them. In your speadsheet, you've actually done the opposite. You've kept more digits than you should have from the Wien's law results and thrown out all but one digit from the Planck results. It's not surprising they don't appear to match (though as ehild noted in his first post, if you round the Wien's law results to one significant figure like you did to the Planck numbers, the results are consistent).