For each statement (a-d) provided below, circle the word choice that correctly describes how the two forms of light compare. a) Infrared light has greater less energy than ultraviolet light. b) X-ray photons have longer/shorter wavelengths than gamma ray photons. c) Visible electromagnetic radiation has a higher/lower frequency than radio wave electromagnetic radiation. d) Infrared light has a faster/slower/ same speed than microwave light.

The graph below represents the relationship between the intensity and wavelength of the sun's electromagnetic radiation.

Which statement is best supported by the graph?

(1) The infrared radiation given off by the sun occurs at a wavelength of 2000 angstroms.

(2) The maximum intensity of radiation given off by the sun occurs in the visible region.

(3) The infrared radiation given off by the sun has a shorter wavelength than ultraviolet radiation.

(4) The electromagnetic energy given off by the sun consists of a single wavelength.

Arbutin, a compound that can be isolated from the leaves of barberry, cranberry, and pear trees, has the molecular formula $\mathrm{C}_{12} \mathrm{H}_{16} \mathrm{O}_{7}.$ When arbutin is treated with aqueous acid or with a $\beta$ -glucosidase, the reaction produces D -glucose and a compound X with the molecular formula $\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{2}.$ The $^{1} \mathrm{H} \mathrm{NMR}$ spectrum of compound $\mathbf{X}$ consists of two singlets, one at $\delta 6.8(4 \mathrm{H})$ and one at $\delta 7.9(2 \mathrm{H}).$ Methylation of arbutin followed by acidic hydrolysis yields 2,3,4,6 -tetra- O-methyl-D-glucose and a compound $\mathbf{Y}\left(\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{O}_{2}\right).$ Compound Y is soluble in dilute aqueous $\mathrm{NaOH}$ but is insoluble in aqueous $\mathrm{NaHCO}_{3}.$ The $^{1} \mathrm{H} \mathrm{NMR}$ spectrum of Y shows a singlet at $\delta 3.9(3 \mathrm{H}),$ a singlet at $\delta 4.8(1 \mathrm{H}),$ and a multiplet (that resembles a singlet) at $\delta 6.8(4 \mathrm{H}).$ Treating compound Y with aqueous NaOH and $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SO}_{4}$ produces compound $\mathrm{Z}\left(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{O}_{2}\right).$ The $^{1} \mathrm{H} \mathrm{NMR}$ spectrum of Z consists of two singlets, one at $\delta 3.75(6 \mathrm{H})$ and one at $\delta 6.8(4 \mathrm{H}).$ Propose structures for arbutin and for compounds $\mathbf{X}, \mathbf{Y},$ and $\mathbf{Z}.$

A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cephei, for which the interval between times of maxi - mum brightness is 5.4 days. The average brightness of this star is 4.0 and its brightness changes by ±0.35. In view of these data, the brightness of Delta Cephei at time t, where t is measured in days, has been modeled by the function

$$B(t)=4.0+0.35sin(2πt/5.4).$$

Find the rate of change of the brightness after t days.

Yellow light of wavelength 589 nm is used to view an object under a microscope. The objective lens diameter is 9.00 mm. (a) What is the limiting angle of resolution? (b) Suppose it is possible to use visible light of any wavelength. What color should you choose to give the smallest possible angle of resolution, and what is this angle? (c) Suppose water fills the space between the object and the objective. What effect does this change have on the resolving power when 589-nm light is used?

Hydrogen has two stable isotopes, ${ }_1^1 \mathrm{H}$ and ${ }_1^2 \mathrm{H}$, and sulfur has four stable isotopes, ${ }_{16}^{32} \mathrm{~S},{ }_{16}^{33} \mathrm{~S},{ }_{16}^{34} \mathrm{~S}$, and ${ }_{16}^{36} \mathrm{~S}$. How many peaks would you observe in the mass spectrum of the positive ion of hydrogen sulfide, $\mathrm{H}_2 \mathrm{~S}^{+}$? Assume no decomposition of the ion into smaller fragments.

This problem is about how strongly matter is coupled to radiation, the subject with which quantum mechanics began. For a simple model, consider a solid iron sphere 2.00 cm in radius. Assume its temperature is always uniform throughout its volume. Assume Wien's law describes the sphere. Although it emits a spectrum of waves having all different wavelengths, assume its power output is carried by photons of wavelength $\lambda_{\max }$. Find the energy of one photon.

This photograph shows an electron micrograph of a giant polytene chromosome. These chromosomes are common in the larval stages of flies, which must grow rapidly before changing to the adult form. Polytene chromosomes form as a result of repeated cycles of DNA replication without cell division. This creates many copies of genes. Within these chromosomes, visible 'puffs' show where there is an active transcription of the genes. (a) What is the consequence of active transcription in a polytene chromosome? (b) Can you think why this might be useful in a larval insect?

Complete each statement using the correct word or words from the vocabulary list. Electromagnetic waves carry ________.

$$\begin{matrix} \text{carrier wave } & \text{microwaves}\\ \text{cathode-ray tube } & \text{photon}\\ \text{electromagnetic wave } & \text{radiant energy }\\ \text{gamma rays } & \text{radio waves }\\ \text{Global Positioning System } & \text{transceiver}\\ \text{infrared waves } & \text{ultraviolet waves }\\ & \text{visible light }\\ & \text{X rays }\\ \end{matrix}$$

A photomultiplier tube (a very sensitive light sensor), is based on the photoelectric effect: incident photons strike a metal surface and the resulting ejected electrons are collected. By counting the number of collected electrons, the number of incident photons (i.e., the incident light intensity) can be determined. If a photomultiplier tube is to respond properly for incident wavelengths throughout the visible range $(410 \mathrm{~nm}$ to $750 \mathrm{~nm})$, what is the maximum value for the work function $W_0(\mathrm{eV})$ of its metal surface?

Two light sources can be adjusted to emit monochromatic light of any visible wavelength. The two sources are coherent, $2.04 \mu \mathrm{m}$ apart, and in line with an observer, so that one source is $2.04 \mu \mathrm{m}$ farther from the observer than the other.(b) How would your answers to part (a) be affected if the two sources were not in line with the observer. but were still arranged so that one source is $2.04 \mu \mathrm{m}$ farther away from the observer than the other?

Suppose that three conformations are proposed for the nonlinear molecule $\mathrm{H}_{2} \mathrm{O}_{3}$ (1, 2, and 3). The infrared absorption spectrum of gaseous $\mathrm{H}_{2} \mathrm{O}_{4}$ has bands at 870, 1370, 2869, and $3417\ \mathrm{cm}^{-1}.$ The Raman spectrum of the same sample has bands at 877, 1408, 1435, and $3407\ \mathrm{cm}^{-1}.$ All bands correspond to fundamental vibrational wavenumbers and you may assume that: (a) the 870 and $877\ \mathrm{cm}^{-1}$ bands arise from the same normal mode, and (b) the 3417 and $3407\ \mathrm{cm}^{-1}$ bands arise from the same normal mode. (i) If $\mathrm{H}_{2} \mathrm{O}_{2}$ were linear, how many normal modes of vibration would it have? (ii) Give the symmetry point group of each of the three proposed conformations of nonlinear $\mathrm{H}_{2} \mathrm{O}_{2}.$ (iii) Determine which of the proposed conformations is inconsistent with the spectroscopic data. Explain your reasoning.

Choose the best answer. For several decades, managers of a forest in West Virginia have selectively logged oak trees in a mixed forest that contains primarily oak and hickory. Which of the following is likely to happen over time? (a) The abundance of mature oak trees in the forest will increase. (b) Large patches of clear-cut forest will become visible from high above the ground. (c) There will be an increase in the abundance of shade-tolerant species. (d) The abundance of older-aged hickory trees will increase.

Coherent light of wavelength $501.5 \mathrm{~nm}$ is sent through two parallel slits in an opaque material. Each slit is $0.700 \mu \mathrm{m}$ wide. Their centers are $2.80 \mu \mathrm{m}$ apart. The light then falls on a semicylindrical screen, with its axis at the midline between the slits. We want to describe the appearance of the light pattern visible on the screen.
(a) Find the direction for each two-slit interference maximum on the screen as an angle away from the bisector of the line joining the slits.