Question

help me 6-27

le) = 13n? –11 +11 6-26. Show that the first few hydrogen atomic orbitals in Table 6.6 are orthonormal. 6-27. Show that the two maxima in the plot of rv ) against r occur at (3 5)(See Figure 6.3.) 6-28. Calculate the value of (r) for the n = 2.7 = 1 state and then 2. 7 0 state of the hydrogen atom. Are you surprised by the answers? Explain.

Answer 1

6-27) The value of r corresponding to the maxima of the curve is called the most probable radius,i.e., rmp .So here we need to find the value of rmp .

For the 23 orbital of t atom, Yes - do 4* (2-5). " where a is the Bohr radius, a=0.53 Å Radial distribution function of as orbital of t is given as RDF = 40m2 4 3 4107** stara (2-a) / Opel og (21) en - [2 (8) ) eryth (27-09) V ( ) (9 IN

d (RDF] (2-3). / [63)-(39)+] At ra maxd (RDF] = 0. dr Now, I to (since it gives a constant value) 803 8 to (since it corresponds to a minimal ér/ao to (since it means o= infinity, which has no physical significance) 2- to (because then r= 2a which is a nodal point and is not possible) or x? - 6a + 4 20 x = -(-6) I J (6) ² - 4x1x4 2x1. [Using the for veula equation?

x=6 ± √ 36-16 2 = 6 + 20 = 6 + 2 5 = 3 +√5 or Pompl = 3 + √5 о or imp = (3+55),