The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is φ (r)= (1/ πao^3) exp (-r/ao)

Required:

a. What is the probability of finding the electron inside a sphere of volume 1.0 pm^3 , centered at the nucleus.

1pm= 10^-12m

b. What is the probability of finding the electron in a volume of 1.0 pm3 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction?

c. What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?

a

step-by-step explanation:

rurbrbrjrnrbjr

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3

hello there!

i believe the answer is

(cot2+1)/sec2=cot2

    csc2/sec2=cot2

  (1/sin2)/(1/cos2)=cot2

  (1/sin2)(cos2/1)=cot2

  cos2/sin2=cot2

  (1/tan2)=cot2

  (cot2)=(cot2)

hope this !

hyperz ^_^