An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Electromagnetic waves' frequency is inversely proportional to their wavelength.
Order the wavelengths from largest (Infrared) to smallest (Gamma).
Reverse the wavelength order to get the frequency order: Infrared (lowest) to Gamma (highest).
Assign the corresponding rank from 1 to 4: Gamma: 4 , Infrared: 1 , X-ray: 3 , Visible light: 2 .
Explanation
Understanding the Problem We are given a table of electromagnetic waves and their corresponding wavelengths in nanometers (nm). Our task is to order these waves from the lowest frequency (1) to the highest frequency (4). We know that frequency and wavelength are inversely proportional, meaning that waves with longer wavelengths have lower frequencies, and waves with shorter wavelengths have higher frequencies.
Plan of Action To solve this problem, we need to compare the wavelengths of the given electromagnetic waves and order them from longest to shortest. This order will then be reversed to obtain the order from lowest to highest frequency.
Listing the Waves and Wavelengths Let's list the electromagnetic waves and their corresponding wavelength ranges:
Gamma: < 1 × 1 0 − 11 nm
Infrared: 7 × 1 0 − 7 to 1 × 1 0 − 3 nm
X-ray: 1 × 1 0 − 11 to 1 × 1 0 − 8 nm
Visible light: 4 × 1 0 − 7 to 7 × 1 0 − 7 nm
Ordering by Wavelength Now, let's order the wavelengths from largest to smallest:
Infrared: 7 × 1 0 − 7 to 1 × 1 0 − 3 nm
Visible light: 4 × 1 0 − 7 to 7 × 1 0 − 7 nm
X-ray: 1 × 1 0 − 11 to 1 × 1 0 − 8 nm
Gamma: < 1 × 1 0 − 11 nm
Determining the Frequency Order Since frequency is inversely proportional to wavelength, we reverse the order to obtain the order from lowest to highest frequency:
Infrared (1)
Visible light (2)
X-ray (3)
Gamma (4)
Final Answer Therefore, the final order from lowest to highest frequency is:
Gamma: 4
Infrared: 1
X-ray: 3
Visible light: 2
Examples
Understanding the electromagnetic spectrum is crucial in various fields. For instance, in medicine, X-rays are used for imaging bones, while infrared radiation is used in thermal imaging to detect temperature variations. In communication, radio waves (a type of electromagnetic wave with even longer wavelengths than infrared) are used to transmit signals. Knowing the order of electromagnetic waves by frequency helps scientists and engineers choose the appropriate type of wave for a specific application.
A total charge of 450 C flows through the device, which leads to approximately 2.81 × 1 0 21 electrons flowing in 30 seconds. This calculation uses the relation between current, charge, and the fundamental charge of an electron.
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