Exam 12: Quantum Mechanics and Atomic Theory

The energy equation for a particle in a cubic box of dimensions L_x = L_y = L_z is E_{nx, ny, nz} = Assume that 8 electrons occupy the allowed energy levels and that 2 electrons can occupy each allowed energy level. A)In the ground state, how many of the 8 electrons have energy equal to ? B)In the ground state, how many of the 8 electrons have energy equal to ? C)In the ground state, how many of the 8 electrons have energy equal to ? D)Calculate the wavelength of light necessary to promote the highest-energy ground-state electron into the lowest-energy excited state. Assume a cubic box with dimensions 1.50 nm * 1.50 nm * 1.50 nm.

From the following list of observations, choose the one that most clearly supports the conclusion that electromagnetic radiation has wave characteristics.

What is the electron configuration of Co³⁺?

Given the electron configurations of the following neutral atoms, identify the element, and state the number of unpaired electrons in its ground state. -[Xe] 4f¹⁴6s²5d²

How many electrons can be described by the quantum numbers n = 3, l = 1?

Which of the following statements is true about the ionization energy of Mg⁺?

Consider the following orderings. I. Al < Si < P < Cl II. Be < Mg < Ca < Sr III. I < Br < Cl < F IV. Na⁺ < Mg²⁺ < Al³⁺ < Si⁴⁺ -Which of these give(s) a correct trend in ionization energy?

Nitrogen has 5 valence electrons. Consider the following electron arrangements. -Which represents the ground state for N?

How many electrons can be contained in all of the orbitals with n = 4?

From the following list of observations, choose the one that most clearly supports the conclusion of de Broglie wavelengths.

What is the electron configuration of indium?

A photographic film needs a minimum of 80.0 kJ/mol for exposure. What is the longest wavelength of radiation with sufficient energy to expose the film?

What is the electron configuration of Ti²⁺?

Which is the highest occupied energy orbital in a silicon atom?

The energy expressions for the electrons in the He⁺ ion and the hydrogen atom are E_n (H) = -a/n² and E_n (He⁺) = -4a/n² Which of the following statements is(are) correct? I. For the transitions , the frequency is larger for H than for He+. II. The first ionization energy of the H atom is smaller than the second. III. The 1s orbital in He+ is larger (in the sense that the probability density is shifted outward) than the 1s orbital in H.

Given the electron configurations of the following neutral atoms, identify the element, and state the number of unpaired electrons in its ground state. -[Kr] 4d¹⁰5s²5p¹

An electron in a one-dimensional box requires energy with wavelength 8080 nm to excite it from the n = 2 energy level to the n = 3 energy level. Calculate the length of the box.

The first ionization energy of Mg is 735 kJ/mol. Calculate Z_eff.

Write the electron configuration for the following: -O^2-

Which of the following statements is(are) true? I. An excited atom can return to its ground state by absorbing electromagnetic radiation. II. The energy of an atom is increased when electromagnetic radiation is emitted from it. III. The energy of electromagnetic radiation increases as its frequency increases. IV. An electron in the n = 4 state in the hydrogen atom can go to the n = 2 state by emitting electromagnetic radiation at the appropriate frequency. V. The frequency and wavelength of electromagnetic radiation are inversely proportional to each other.