I would like to use Find Root on the following expression. Any help would be appreciated.
elctrn[eV_]:=6.62610^-34/Sqrt[2.09.1110^-31eV1.610^-19]100.0;
FindRoot[elctrn[eV],{eV,6.1410^-9},AccuracyGoal->4,PrecisionGoal->4]
instantly returns
{eV->4.47606*^-6}
Thanks for your help and enthusiasm. Unfortunately, the correct answer is: 398.8 electron volts (I worked the answer out by trial and error). Then I thought to try âFindRootâ.
Your expression is always positive.
Thank you very much for your input. I found, by trial and error, an electron Volt level of 399.8 electron volts returns the correct answer: 6.14 x 10^-9.
All I see are images and I will not attempt to reenter them by hand. As written, it wonât have a solution. Even after the definition gets fixed (in a way that makes this have an actual answer),it looks like the problem will still have really bad scaling.
Thank you, sir for your kind attention to my issues. I tried other alternatives, like: AccuracyGoal-> Infinity and WorkingPrecision->MachinePrecision. Nothing seems to work. If I start things off with elctrn[eV_]:= I do indeed get a numerical answer. {eV â 4.476 x 10^-6} free of error messages. Unfortunately, the correct answer (arrived at through trial and error) is 399.8 electron volts. Am I using the wrong version of Scientific Notation for my numbers? The equation in question is a popular rewrite of De Broglieâs expression for particle wavelength in terms of electron volts. Not much I can do about the magnitude of the terms. I apologize to you for all the trouble Iâm causing to the Mathematica community.
What steps did you use to arrive at 398.8?
Trial and error. Please note. I started in with Mathematica in 2002. Never had a problem I couldnât solve by reading your tutorials. Soon as I upgraded to Windows 11 Pro in November of 2022 things went south. I suspect very few of your clients are on Windows 11 Pro. Thus, you never get complaints. Except from me.
âTrial and errorâ is not âshowing stepsâ. Also I doubt any issue with this example involves Windows 11 Pro. This looks to be strictly a kernel evaluation, with the user interface particulars not implicated.
First. I am relieved to learn you are not finding any conflict between Mathematica 13 and Windows 11 Pro. Second. A great many years ago a Nobel Laureate, Arthur Holly Compton made a careful study of the relationship between the dominant wavelength in an X Ray range energy field and the production of âRecoil Electronsâ at a given wavelength. My goal, to explain his findings in terms of the De Broglie wave / particle equations in units of electron volts. Among other wavelengths Compton reported 0.614 Angstroms (6.14 x 10 ^-9 centimeters) as especially productive of âRecoil Electronsâ. I wrote the equation (above) to search for the amount of energy in units of electron volts needed to produce non-relativistic waves at a wavelength of 0.614 angstroms. Before I tried âFindRootâ I entered different values into the electron volt term (eV) in the equation above at the top of the page. A few minutes of labor and I arrived at 399.8 electron volts as able to produce X ray waves at 0.614 angstroms. Then I tried FindRoot. Your expression returns an unlikely value of 4.7 x 10^-6. So, next, I posted this plea for help.
elctrn[eV_] :=
6.62610^-34/Sqrt[2.09.1110^-31eV1.610^-19]*100.0;
productiveValue = 6.14 10^-9;
Solve[elctrn[ev] == productiveValue]
FindRoot[elctrn[ev] == productiveValue, {ev, 6.14 10^-9}]
To summarize, the equation you posted had elctrn[eV]==0 whereas, as Gianluca Gorni shows, you most likely intended it to be elctrn[eV]==6.14 10^-9. Which gives a solution very close to the one you had obtained by plugging in possible values.
Professor Daniel Lichtblau, Wolfram Research
Please be patient. I am going to explore the solution offered up by Professor Gianluca Gorni. I will get back to both of you at some time later in the week. Thanks again.