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(4 pts) In either chemistry or physics so far, you've probably learned about the orbital model of atoms

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(4 pts) In either chemistry or physics so far, you've probably learned about the orbital model of atoms. Consider a hydrogen atom in the "35" state. The probability to observe the electron between a radius r = 0 and a radius r = an from the nucleus is: no I = ?r) air (1} a where: 4r2 r r2 2 2,. : — — — — _ 1'3"" ?r} 390% [27 18:1,} +23%] 3 (2} Here, an : 0.0529 nm is a constant called the Bshr radius, which is the most likely radius for the electron in the ground state (the 1s state}. This integral can be done analytically, but it's much easier to do numerically. (a) {2 pts) Rewrite the integral in dimensionless form using an appropriate u—substitution. Hint: What are the dimensions of r? Is there another constant in the integral with the same dimensions?

Your integral should now have all the constants outside the integral and look like: I = (constants) - fumu 9(a) do (3) 15min {you need to determine 9(a), the constants, and ?ll in the appropriate integration limits, can and mama). b) {1 pt) Write a MATLAB function for 9(a). You can use either an inline function, or a script. :c) {1 pt) Numerically etmluate ?r" 9(a) do; using your function from (b) in combi— nation with MATLAB's integral. Now multiply,r by the constants to get your ?nal answer. State your answer to 5 signi?cant ?gures.