Light, Energy, and the Hydrogen Atom

a. Which has the greater wavelength, blue light or red light?

b. How do the frequencies of blue light and red light compare?

c. How does the energy of blue light compare with that of red light?

d. Does blue light have a greater speed than red light?

e. How does the energy of three photons from a blue light source compare with the energy of one photon of blue light from the same source? How does the energy of two photons corresponding to a wavelength of 451 nm (blue light) compare with the energy of three photons corresponding to a wavelength of 704 nm (red light)?

Energy of two Blue photons corresponds to the wavelength, λ = 451 x ?10?^(-9) m

Energy of three Red protons corresponds to the wavelength, λ = 704 x ?10?^(-9) m

f. A hydrogen atom with an electron in its ground state interacts with a photon of light with a wavelength of 1.22 × 10-6m. Could the electron make a transition from the ground state to a higher energy level? If it does make a transition, indicate which one. If no transition can occur, explain.

g. If you have one mole of hydrogen atoms with their electrons in the n = 1 level, what is the minimum number of photons you would need to interact with these atoms in order to have all of their electrons promoted to the n = 3 level? What wavelength of light would you need to perform this experiment?

Investigating Energy Levels

Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation

E = - (RH / n3)

whereRHis the same as for hydrogen (2.179 ×10-18J). Answer the following questions, without calculating energy values.

a. How would the ground-state energy levels of X and H compare?

b. Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer.

c. How do the spacings of the energy levels of X and H compare?

d. Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom?

e. Which atom, X or H, would require more energy to completely remove its electron?

f. A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 2 to n = 5) in an atom of X? Explain.

Concept Explorations

A hypothetical element, X, has the following ionization energy values:

First ionization energy: 900 kJ/mol
Second ionization energy: 1750 kJ/mol
Third ionization energy: 14,900 kJ/mol
Fourth ionization energy: 21,000 kJ/mol
Another element, Y, has the following ionization energy values:
First ionization energy: 1200 kJ/mol
Second ionization energy: 2500 kJ/mol
Third ionization energy: 19,900 kJ/mol
Fourth ionization energy: 26,000 kJ/mol

a. To what family of the periodic table would element X be most likely to belong? Explain?

b. What charge would you expect element X to have when it forms an ion?

c. If you were to place elements X and Y into the periodic table, would element Y be in the same period as element X? If not in the same period, where might they be relative to each other in the periodic table?

d. Would an atom of Y be smaller or larger than an atom of X? Explain your reasoning.

Periodic Properties II

Consider two hypothetical elements, W and Z. Element W has an electron affinity of -150 kJ/mol, and element Z has an electron affinity of -38 kJ/mol.

a. If you have a W- ion and a Z- ion, from which ion would it require more energy to remove an electron? Explain your answer.

b. If elements W and Z are in the same period of the periodic table, which atom would you expect to have the greater atomic radius? Why?

c. Assuming that the elements are in the same period, which element would you expect to have the smaller first ionization energy?

d. Do the valence electrons in element Z feel a greater effective nuclear charge than those in element W? Explain how you arrived at your answer.