Atomic Orbitals and Pauli Exclusion Principle

What is the radial distribution function P(r) in terms of R(r)?

P(r) = r2 R(r)2

What is the condition for an electron to occupy a particular orbital in a many-electron atom?

The electron must occupy the lowest energy level.

What is the condition for a spectroscopic transition to occur between two energy levels?

∆n = any, ∆l = ±1, ∆ml = 0, ±1

What is the shape of the dz2 orbital?

The dz2 orbital is 3z2-r2 shaped. Signup and view all the answers

What is the overall wave function of a many-electron atom?

The product of atomic orbitals. Signup and view all the answers

What is the value of the energy of the first energy level in terms of the Rydberg constant?

-hcRH Signup and view all the answers

What is the ionization energy of hydrogen in terms of the Rydberg constant?

hcRH Signup and view all the answers

What is the number of orbitals in a shell with principal quantum number n?

n^2 Signup and view all the answers

What is the form of the radial wavefunction Rn,l(r) in terms of the polynomial and exponential decay?

N x (polynomial in r) x exp(-ρ/2) Signup and view all the answers

What is the property of the radial wavefunction Rn,l(r) as r approaches infinity?

R approaches zero Signup and view all the answers

What is the physical significance of the Bohr radius in the hydrogenic atom?

It defines a length-scale for the wavefunction Signup and view all the answers

What is the relationship between the ionization energy and the energy levels of an atom?

The ionization energy is the energy required to remove an electron from the highest occupied shell Signup and view all the answers

What is the role of the reduced mass in the Schrödinger equation for hydrogenic atoms?

It takes into account the mass of the electron and the nucleus Signup and view all the answers

What is the purpose of the emission spectrum in understanding the energy levels of an atom?

It provides experimental information about the energy levels of the atoms Signup and view all the answers

What is the physical significance of the Rydberg constant in the hydrogenic atom?

It is a measure of the frequency of the emitted photon Signup and view all the answers

What is the relationship between the mean radius of an orbital and the atomic number?

It decreases with the atomic number Signup and view all the answers

What is the probability density of finding an electron at a point in a 1s orbital?

|Ψ|^2 Signup and view all the answers

What is the shape of the 1s orbital?

Spherical symmetric Signup and view all the answers

What is the probability of finding the electron in a volume of ∆V in a 1s orbital?

|Ψ|^2 ∆V Signup and view all the answers

What is the relation between the principal quantum number n and the energy levels of an electron?

Energy levels depend only on the principal quantum number n Signup and view all the answers

What is the radial distribution function for an electron in a spherical orbital?

4πr^2|R(r)|^2 Signup and view all the answers

What does the Rydberg constant represent?

The change of energy when an electron drops from one principal quantum number to another Signup and view all the answers

What is the significance of the boundary condition R(r) → 0 as r → ∞?

It introduces the principal quantum number n Signup and view all the answers

What is the relation between the atomic number Z and the energy levels of an electron?

Energy levels depend on Z^2 Signup and view all the answers

What is the shape of the wavefunction Y(φ, θ) for an electron in an atom?

Same as the rotation on a sphere Signup and view all the answers

What is the significance of the Rydberg constant in atomic spectra?

It is a mathematical constant that relates the energy levels of an atom Signup and view all the answers

What happens to an atom when it absorbs energy in an emission spectrum experiment?

It gains energy and moves to a higher energy state Signup and view all the answers

What is the characteristic of the energy levels described by the Rydberg formula?

They are discrete and have specific values Signup and view all the answers

What is the role of atomic shells in describing the arrangement of electrons in an atom?

They are used to describe the arrangement of electrons in energy levels Signup and view all the answers

What is the characteristic of the wavefunction of a hydrogenic atom?

It is a simple function that can be solved analytically Signup and view all the answers

What is the maximum number of electrons that can occupy a given orbital according to the Pauli Exclusion Principle?

Two Signup and view all the answers

What is the name of the principle that explains how electrons are arranged in an atom?

Pauli Exclusion Principle Signup and view all the answers