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Problem(Set(07(–(Light,(Quantum(Theory! Chem!105! 1. (a) Explain what a photon is in 1-3 sentences. A photon is one quanta of light, or in other words, a packet of radiant energy (electromagnetic radiation) with energy proportional to its frequency: E=hγ (b) What does it mean for something to be ‘quantized’? The number of possible values or states is restricted; certain variables can only have certain discrete magnitudes (or in other words, particular, regularly-spaced values). (c) Give examples of 3 everyday things that are quantized (for example, stairs are quantized). Examples: stairs, ladder, class rank (you can be either #1 or #2 in the class, not in between), number of family members, number of students at BYU or in this class… Ask yourself whether it makes sense for something to NOT be a whole #. If the answer is no, then that something is quantized.

2. Complete the following table. If the wavelength is given, calculate the frequency of a photon of that wavelength, and vice versa. Then calculate the energy of 1000 photons of that wavelength or frequency. Label what part of the electromagnetic (EM) spectrum each photon is in. If it is in the visible region, state what color. Wavelength Frequency (Hz, or s-1) 100. m 2.99 x 10^6 1.00 m 2.99 x 10^8 1.00 cm 3.0 x 10^10 1.00 mm 3.0 x 10^11 1.00 µm 3.0 x 10^14 750 nm 4.0 x 10^14 585 nm 5.12 x 10^14 455 nm 6.59 × 1014 306 nm 9.78 × 1014 100. nm 3.0 x 10^15 1.00 nm 3.0 x 10^17

E of 1000 photons (J) 1.98 x 10^-24 1.98 x 10^-22 1.98 x 10^-20 1.98 x 10^-19 1.98 x 10^-16 2.65 x 10^-16 3.40 x 10^-16 4.37 × 10-16 6.48 × 10-16 1.98 x 10^-15 1.98 x 10^-13

EM range radio radio microwave Infra-red UV or x-ray Visible, red Visible, yellow Visible, blue UV UV X-ray

3. A typical microwave oven operates at 2.45 GHz. (a) Calculate the wavelength of this electromagnetic radiation. 1-𝑠 𝑐 2.9979 ⋅ 10, -𝑚 100𝑐𝑚 = 12.2-𝑐𝑚 𝜆= = = 0.122-𝑚-𝑥 2 𝑠 1𝑚 2.45 ⋅ 10 𝜈 (b) The microwave in Dr. Smith’s office is about 30.5cm wide. How many wavelengths does it take for the wave to travel the length of the microwave and back? Total length = 30.5cm x 2 = 61cm. 61cm / 12.2cm/wavelength = 5 wavelengths (c) How many nodes occur for the wave inside the microwave? Drawing a picture may be helpful. 4 nodes. Note that the total number of nodes equals n-1, where n is the number of wavelengths that fit inside the boundaries.

(d) Do the nodes for waves travelling in the forward and reverse directions line up (i.e., does the wave form a standing wave)? Yes! (e) What happens to food placed at the nodes? At the nodes, wave amplitude is zero so it’s as if there is no wave; thus food at nodes does not heat up. (f) Why do we spin food inside the microwave? We spin food in the microwave to avoid uneven heating; spinning prevents parts of the food from getting stuck in nodes and not heating up. 4. The 3 centimeter band is a portion of the radio spectrum that is allocated to amateur radio and amateur satellite enthusiasts. What is the frequency of electromagnetic radiation with a wavelength of 3.00 cm? How does this compare to the 60 Hz frequency of the oscillations of alternating current (AC) from our electrical power grid? We know that c = ln, so we can rearrange this to get 𝜈 = = 10.0-𝐺𝐻𝑧

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