Consider the 4pz orbital for the hydrogen atom (Z=1).

a) How many angular nodes does this orbital have? Identify the geometric shape and location of all angular nodes.

b) The radial portion of the wave function for this orbital is listed below:

R(r) = [1/ao^3/2/ (0.0645) ] [( 5-5p+p^2]p(e-p) p= (2 Z /n(ao))r
n=principle quantum number
**How many radial nodes does this orbital have?
c)what are the values of r for the radial node(s)? Express r in both units of ao and angstroms.

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Related questions

consider the 7p(z) orbital. a0 list the quantum numbers for an electron in this state. b) list all degenerate orbitals for an electron in this state. c) how many radial nodes does this orbital have? d) how many angular nodes does this orbital have? e) write the complete hydrogen wavefunction for this orbital. f) sketch the radial wavefunction for this orbital.

The probability of finding an electron at a point in an atom is referred to as the probability density (Ï2). The spatial distribution of these densities can be derived from the radial wave function R(r) and angular wave function Y(Î¸,Ï), then solving the SchrÃ¶dinger equation for a specific set of quantum numbers.

Which of the following statements about nodes and probability density are accurate?

	a-The 2s orbital does not have any nodes.
	b-The probability of finding an electron at the center of a p orbital is zero.
	c-The 3p orbitals have two nodes.
	d-The probability of finding an electron at the center of a d orbital is greater than zero.
	e-The 4f orbitals have three nodes.

1) What are the possible orbitals for n=3?

s, p, d
s, p, d, f
s
s, p

2) What value of ℓ is represented by a d orbital?

3) How many orbitals are contained in the third principal level (n=3) of a given atom?

4) Which of the following statements is TRUE?

The principal quantum number (n) describes the shape of an orbital.
The angular momentum quantum number (ℓ) describes the size and energy associated with an orbital
The magnetic quantum number (mℓ) describes the orientation of the orbital.
An orbital is a path that an electron follows during its movement in an atom
All of the above are true

5) Which of the following transitions represents the emission of a photon with the largest energy?

n=2 to n=1
n=3 to n=1
n=6 to n=4
n=1 to n=4
n=2 to n=4

6) Choose the transition (in a hydrogen atom) below that represents the absorption of the shortest wavelength photon.

n=1 to n=2
n=2 to n=3
n=4 to n=5
n=6 to n=3
n=3 to n=1

7) Each of the following sets of quantum numbers is supposed to specify an orbital. Choose the one set of quantum numbers that does not contain an error.