Chapter 5

Objects get their colors from reflecting only certain wavelengths when hit with white light. Light reflected from a green leaf is found to have a wavelength of \(4.90 \times 10^{-7} \mathrm{m} .\) What is the frequency of the light?

X rays can penetrate body tissues and are widely used to diagnose and treat disorders of internal body structures. What is the frequency of an \(\mathrm{X}\) ray with a wavelength of \(1.15 \times 10^{-10} \mathrm{m}\) ?

Calculate the energy possessed by a single photon of each of the following types of electromagnetic radiation. a. \(6.32 \times 10^{20} \mathrm{s}^{-1} \quad\) b. \(9.50 \times 10^{13} \mathrm{Hz} \quad\) c. \(1.05 \times 10^{16} \mathrm{s}^{-1}\)

The blue color in some fireworks occurs when copper(1) chloride is heated to approximately 1500 \(\mathrm{K}\) and emits blue light of wavelength \(4.50 \times 10^{2} \mathrm{nm} .\) How much energy does one photon of this light carry?

Describe the phenomena that can be explained only by the particle model of light.

Compare and contrast continuous spectrum and emission spectrum.

Discuss the way in which Einstein utilized Planck’s quantum concept to explain the photoelectric effect.

Calculate Heating 235 \(\mathrm{g}\) of water from \(22.6^{\circ} \mathrm{C}\) to \(94.4^{\circ} \mathrm{C}\) in a microwave oven requires \(7.06 \times 10^{4} \mathrm{J}\) of energy. If the microwave frequency is \(2.88 \times 10^{10} \mathrm{s}^{-1}\) , how many quanta are required to supply the \(7.06 \times 10^{4} \mathrm{J} ?\)

Explain the reason, according to Bohr’s atomic model, why atomic emission spectra contain only certain frequencies of light.

Differentiate between the wavelength of visible light and the wavelength of a moving soccer ball.

Explain why the location of an electron in an atom is uncertain using the Heisenberg uncertainty principle and de Broglie’s wave-particle duality. How is the location of electrons in atoms defined?

Compare and contrast Bohr’s model and the quantum mechanical model of the atom.

Write ground-state electron configurations for the following elements. a. bromine (Br) c. antimony (Sb) e. terbium (Tb) b. strontium (Sr) d. rhenium (Re) f. titanium (Ti)

A chlorine atom in its ground state has a total of seven electrons in orbitals related to the atom’s third energy level. How many of the seven electrons occupy p orbitals? How many of the 17 electrons in a chlorine atom occupy p orbitals?

When a sulfur atom reacts with other atoms, electrons in orbitals related to the atom’s third energy level are involved. How many such electrons does a sulfur atom have?

An element has the ground-state electron configuration \([\mathrm{Kr}] 5 \mathrm{s}^{2} 4 \mathrm{d}^{10} 5 \mathrm{p}^{1} .\) It is part of some semiconductors and used in various alloys. What element is it?

Challenge In its ground state, an atom of an element has two electrons in all orbitals related to the atom’s highest energy level for which n = 6. Using noble-gas notation, write the electron configuration for this element, and identify the element.

Draw electron-dot structures for atoms of the following elements. a. magnesium b. thallium c. xenon

An atom of an element has a total of 13 electrons. What is the element, and how many electrons are shown in its electron-dot structure?

Apply the Pauli exclusion principle, the aufbau principle, and Hund’s rule to write out the electron configuration and draw the orbital diagram for each of the following elements. a. silicon b. fluorine c. calcium d. krypton

Define valence electron

Extend the aufbau sequence through an element that has not yet been identified, but whose atoms would completely fill 7p orbitals. How many electrons such an atom would have? Write its electron configuration using noble-gas notation for the previous noble gas, radon.

Define the following terms. a. frequency c. quantum b. wavelength d. ground state

Arrange the following types of electromagnetic radiation in order of increasing wavelength. a. ultraviolet light c. radio waves b. microwaves d. X rays

What is the photoelectric effect?

Neon Sign How does light emitted from a neon sign differ from sunlight?

Explain Planck’s quantum concept as it relates to energy lost or gained by matter.

How did Einstein explain the photoelectric effect?

Rainbow What are two differences between the red and green electromagnetic waves in a rainbow?

Temperature What happens to the light emitted by a heated, glowing object as its temperature increases?

What are three deficiencies of the wave model of light related to light’s interaction with matter?

How are radio waves and ultraviolet waves similar? How are they different?

What is the wavelength of electromagnetic radiation with a frequency of \(5.00 \times 10^{12} \mathrm{Hz}\) ? What kind of electromagnetic radiation is this?

What is the frequency of electromagnetic radiation with a wavelength of \(3.33 \times 10^{-8} \mathrm{m} ?\) What type of electromagnetic radiation is this?

What is the speed of an electromagnetic wave with a frequency of \(1.33 \times 10^{17} \mathrm{Hz}\) and a wavelength of 2.25 \(\mathrm{nm}\) ?

What is the energy of a photon of red light that has a frequency of \(4.48 \times 10^{14} \mathrm{Hz?}\)

What is the energy of an ultraviolet photon that has a wavelength of \(1.18 \times 10^{-8} \mathrm{m} ?\)

A photon has an energy of \(2.93 \times 10^{-25} \mathrm{J}\) . What is its frequency? What type of electromagnetic radiation is the photon?

A photon has an energy of \(1.10 \times 10^{-13}\) J. What is the photon's wavelength? What type of electromagnetic radiation is it?

Spacecraft How long does it take a radio signal from the Voyager spacecraft to reach Earth if the distance between Voyager and Earth is \(2.72 \times 10^{9} \mathrm{km} ?\)

Radio Waves If your favorite FM radio station broadcasts at a frequency of 104.5 MHz, what is the wavelength of the station’s signal in meters? What is the energy of a photon of the station’s electromagnetic signal?

Platinum What minimum frequency of light is needed to eject a photoelectron from atoms of platinum, which require at least \(9.08 \times 10^{-19} \mathrm{J} /\) photon?

Eye Surgery The argon fluoride (ArF) laser used in some refractive eye surgeries emits electromagnetic radiation of 193.3 nm wavelength. What is the frequency of the ArF laser’s radiation? What is the energy of a single quantum of the radiation?

According to the Bohr model, how do electrons move in atoms?

What does \(n\) designate in Bohr's atomic model?

What is the difference between an atom’s ground state and an excited state?

What is the name of the atomic model in which electrons are treated as waves? Who first wrote the electron wave equations that led to this model?

What does \(n\) represent in the quantum mechanical model of the atom?

How many energy sublevels are contained in each of the hydrogen atom’s first three energy levels?

What atomic orbitals are related to a d sublevel?