To understand what's happening on the macroscopic level, we have to dive deep and explore the world of atoms and molecules. In this topic, we will introduce concepts that deal with the wave nature of matter and light, and the energy requirements for transitions of electrons between different energy levels surrounding the nucleus of an atom.
- Calculate the wavelength of electromagnetic radiation given its frequency or its frequency given its wavelength. (6.1)
- Order the common kinds of radiation in the electromagnetic spectrum according to their wavelengths or energy. (6.1)
- Explain what photons are and be able to calculate their energies given either their frequency or wavelength. (6.2)
- Explain how line spectra relate to the idea of quantized energy states of electrons in atoms. (6.3)
As we begin this topic, make sure to skim the text and take down notes. The key ideas are presented in the slides below, which correspond to sections 6.1-6.3 of the text.
Now that you've seen the content, work out the sample and practice problems below (from 6.1-6.4 of the text).
To wrap up this mission, work out the mastery problems below on a separate sheet of paper, then turn in all of your stamped work on OneNote. These problems come from the back of chapter 6 in your book.
6.28 A stellar object is emitting radiation at 3.55 mm.
(a) What type of electromagnetic spectrum is this radiation?
(b) If the detector is capturing 3.2×108 photons per second at this wavelength, what is the total energy of the photons detected in one hour?
6.30 Sodium metal requires a photon with a minimum energy of 4.41×10-19 J to emit electrons.
(a) What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect?
(b) What is the wavelength of this light?
(c) If sodium is irradiated with light of 439 nm, what is the maximum possible kinetic energy of the emitted electrons?
(d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is 1.00 μJ?
6.36 For each of the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed during the transition:
(a) from n = 4 to n = 1
(b) from n = 5 to n = 2
(c) from n = 3 to n = 6
Does any transition above emit or absorb visible light?
6.40 The hydrogen atom can absorb light of wavelength 2626 nm.
(a) In what region of the electromagnetic spectrum is this absorption found?
(b) Determine the initial and final values of n associated with this absorption.
6.75 Consider the two waves shown here, which we will consider to represent two electromagnetic radiations:
(a) What is the wavelength of wave A? Of wave B?
(b) What is the frequency of wave A? Of wave B?
(c) Identify the regions of the electromagnetic spectrum to which waves A and B belong.
6.99 Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food.
(a) Suppose that the microwave radiation has a wavelength of 11.2 cm. How many photons are required to heat 200 mL of coffee from 23 °C to 60 °C?
(b) Suppose the microwave’s power is 900 W (1 Watt = 1 joule/second). How long would you have to heat the coffee in part (a)?
Congratulations Visitor! You've mastered the first mission of this topic. Keep it up!