One of the watershed events in the development of physics and chemistry wasthe

Chapter 6, Problem 6-20

(choose chapter or problem)

One of the watershed events in the development of physics and chemistry wasthe appearance of Einstein's landmark paper explaining the photoelectric effect,establishing the corpuscular nature of light, and leading to the modern view ofthe wave-particle duality of the microscopic realm.(a) Look up Millikan's paper on the photoelectric effect, and describe how hecharacterized Einstein's work.6(b) In Section 6C-l we described how measurements of the stopping voltage ina photo tube as a function of frequency can be used to determine Planck'sconstant. Describe and discuss three experimental diffic!ulties in the determinationof the Planck constant by this method. You may find the paper byKeesing 7 useful in this discussion.(c) Use the data in Table III of Millikan's paper to determine the stopping potentialas a function of wavelength at 433.9, 404.7, 365.0, 312.5, and 253.5 nm.(d) Enter these data into an Excel spreadsheet, and perform a least-squaresanalysis of the data to determine Planck's constant and its uncertainty. Compareyour results to those of Millikan, and discuss any differences.(e) One of the difficulties that you discovered in (b) and (c) is related to the determinationof the stopping potential. Knudsen 8 has described a methodbased on the following normalized equations ':41Tmk2T' ( e" e.18 )"'(8) = --h-'- e' - 2.' + 3' - ...where "'(8) is normalized photocurrent and 8 is the normalized retardingvoltage in units of kT. Create a spreadsheet, and generate a plot of<1>(8)= log "'(8) versus [; for 56 values in the range [; = - 5 to 8 = 50. Alsoplot the following normalized data collected at 365.015 nm."o,kT logq,fo)33.2~ 01733.87 0.333~72 0.533SA6 07936.20 0.9936.93 12037.67 1.3938.41 1.5840.43 1.9742.3~ 2.2744.25 2.4746.16 2.6447.97 2.7749.99 2.8951.90 3.0153.82 3.1055.63 3.1957.65 3.2559.56 3.3361.48 3.3863.29 3.4465.31 3.5167.23 3.5469.04 3.60(h) Planck's constant is no longer determined by measurements on photocells.How is it determined? 10 What other fundamental constants depend onPlanck's constant? What are the current values of these constants, and whatare their uncertainties""(i) Least-squares procedures can be used to adjust the values of the fundamentalconstants so that they are internally consistent.1' Describe how this proceduremight be accomplished. How does an improvement in the quality of the measurementof one constant such as Avogadro's number affect the values of theother constants?(j) Over the past several decades, much effort has been expended in the determinationof the values of the fundamental constants. Why is this effort importantin analytical chemistry, or why is it not? What measurable quantities inanalytical chemistry depend on the values of the fundamental constants?Why are these efforts important to science and to the world at large"" Commentcritically on the return on the investment of time and effort that hasgone into the determination of the fundamental constants.Print two copies of the plot in full-page format, and overlay the two copiesover a hght source. Determine the stopping potential at 365.015 nm as descnbedby Knudsen. Compareyour result with his result in the table in (f).Perform a least-squares analySISof the data in the following table to determmePlanck's constant. Compare these results to those of Millikan and yourresults from (c). Rallonahze any differences in thc results in terms of experimentaldifferences and other fundamental considerations.A,nm kT V435.834 56.7 [,47340~.656 48.1 1.249365.015 35.4 0.919334.14K 23.4 0.608313.170 14.0 0.364296.728 5.8 0.151289.36 1.3 0.034(g) There is an element of circular reasoning in the Knudsen procedure. Describeand diSCUSScfItIcally the use of the curve-matching process to determine thestoppmg potential."