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Chapter 8: Problem 23

In what region of the electromagnetic spectrum would you expect to find radiation having an energy per photon 100 times that associated with 988 nm radiation?

Short Answer

Expert verified
The radiations is in the region of \(x\) on the electromagnetic spectrum. (Replace \(x\) with the specific region e.g ultraviolet.)

Step by step solution

01

Calculate the Energy of 988nm radiation

First, the energy of the radiation with a wavelength of 988nm needs to be calculated. Using the formula for energy of a photon, \(E = h * \frac{c}{\lambda}\), where \(h\) is the Planck's constant \(6.63 * 10^{-34} Js\), \(c\) is the speed of light \(3.0 * 10^8 m/s\), and \(\lambda\) is the wavelength which is 988nm or \( 988 * 10^{-9}m \).
02

Calculate the energy of the given radiation

The problem states that the energy of the given radiation is 100 times that of 988nm radiation. So, multiply the energy obtained in the first step by 100.
03

Calculate the wavelength of the given radiation

Since energy and wavelength are in a reciprocal relationship, the wavelength of the given radiation can be found after obtaining its energy. Rearrange the energy formula to solve for wavelength, \(\lambda = h * \frac{c}{E}\). Insert the energy from step 2 into the formula to get the wavelength.
04

Identify the region of the electromagnetic spectrum

With the obtained wavelength of the radiation, its corresponding region on the electromagnetic spectrum can be identified.

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Most popular questions from this chapter

Which must possess a greater velocity to produce matter waves of the same wavelength (such as \(1 \mathrm{nm}\) ), protons or electrons? Explain your reasoning.

Which of the following statements is (are) correct for an electron with \(n=4\) and \(m_{\ell}=2 ?\) Explain. (a) The electron is in the fourth principal shell. (b) The electron may be in a \(d\) orbital. (c) The electron may be in a \(p\) orbital. (d) The electron must have \(m_{s}=+\frac{1}{2}\)

The magnesium spectrum has a line at \(266.8 \mathrm{nm}\). Which of these statements about this radiation is (are) correct? Explain. (a) It has a higher frequency than radiation with wavelength \(402 \mathrm{nm}\) (b) It is visible to the eye. (c) It has a greater speed in a vacuum than does red light of wavelength \(652 \mathrm{nm}\) (d) Its wavelength is longer than that of X-rays.

The lowest-frequency light that will produce the photoelectric effect is called the threshold frequency. (a) The threshold frequency for indium is \(9.96 \times\) \(10^{14} \mathrm{s}^{-1} .\) What is the energy, in joules, of a photon of this radiation? (b) Will indium display the photoelectric effect with UV light? With infrared light? Explain.

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) \(6.72 \mu \mathrm{m}\)
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