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Chapter 8: Problem 6

Without doing detailed calculations, arrange the following electromagnetic radiation sources in order of increasing frequency: (a) a red traffic light, (b) a \(91.9 \mathrm{MHz}\) radio transmitter, (c) light with a frequency of \(3.0 \times 10^{14} \mathrm{s}^{-1}\) (d) light with a wavelength of \(49 \mathrm{nm}\).

Short Answer

Expert verified
The arranged order of increasing frequency is: a 91.9 MHz radio transmitter (b), light with a frequency of \(3.0 \times 10^{14} s^{-1}\) (c), a red traffic light (a), and light with a wavelength of \(49 nm\) (d).

Step by step solution

01

Frequency of a radio transmitter

Given that (b) a radio transmitter operates at \(91.9 \mathrm{MHz}\), which is equal to \(91.9 \times 10^{6} \mathrm{s^{-1}}\).
02

Frequency of red light

Light from a red traffic light (a) is at the lower frequency end of the visible spectrum, with a frequency approximately around \(4.3 \times 10^{14} \mathrm{s^{-1}}\).
03

Frequency of light

For (c), we are already given light with a frequency of \(3.0 \times 10^{14} \mathrm{s}^{-1}\).
04

Frequency with a wavelength of 49 nm

Using the wave equation and the value of the speed of light \( v = 3.0 \times 10^8 m/s \), the light of wavelength \(49 \mathrm{nm}\) (d) has a frequency \(f = v/\lambda = (3.0 \times 10^{8} m/s) / (49 \times 10^{-9} m) = 6.12 \times 10^{15} \mathrm{s^{-1}}\).
05

Arranging in order of increasing frequency

Arranging these in order of increasing frequency: a radio transmitter (b), light of frequency \(3.0 \times 10^{14} s^{-1}\) (c), red traffic light (a), and light of wavelength \(49 nm\) (d).

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Most popular questions from this chapter

Explain the important distinctions between each pair of terms: (a) frequency and wavelength; (b) ultraviolet and infrared light; (c) continuous and discontinuous spectra; (d) traveling and standing waves; (e) quantum number and orbital; (f) spd f notation and orbital diagram; (g) \(s\) block and \(p\) block; (h) main group and transition element; (i) the ground state and excited state of a hydrogen atom.

In everyday usage, the term "quantum jump" describes a change of a very significant magnitude compared to more gradual, incremental changes; it is similar in meaning to the term "a sea change." Does quantum jump have the same meaning when applied to events at the atomic or molecular level? Explain.

Without doing detailed calculations, indicate which of the following electromagnetic radiations has the greatest energy per photon and which has the least: (a) \(662 \mathrm{nm}\) (b) \(2.1 \times 10^{-5} \mathrm{cm} ;\) (c) \(3.58 \mu \mathrm{m} ;\) (d) \(4.1 \times 10^{-6} \mathrm{m}\).

Without doing detailed calculations, determine which of the following wavelengths represents light of the highest frequency: (a) \(6.7 \times 10^{-4} \mathrm{cm} ;\) (b) \(1.23 \mathrm{mm}\) (c) \(80 \mathrm{nm} ;\) (d) \(6.72 \mu \mathrm{m}\)

A standing wave in a string \(42 \mathrm{cm}\) long has a total of six nodes (including those at the ends). What is the wavelength, in centimeters, of this standing wave?
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