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Chapter 15: Problem 2166

The frequency \(1057 \mathrm{MHz}\) of radiation arising from two close energy levels in hydrogen belongs to (A) radio waves (B) infrared waves (C) micro waves (D) \gamma rays

Short Answer

Expert verified
The given frequency is \(1057 MHz\), which equals \(1057 \times 10^6\) Hz. Comparing this with the frequency ranges of different electromagnetic waves, it falls within the range of radio waves (< \(10^9\) Hz). Therefore, the radiation belongs to (A) radio waves.

Step by step solution

01

Convert the frequency to Hz

Given the frequency is 1057 MHz, convert megahertz (MHz) to hertz (Hz) by multiplying by \(10^6\): Frequency = \(1057 \times 10^6\) Hz
02

Compare the frequency with the frequency ranges of electromagnetic waves

We will now compare the given frequency of \(1057 \times 10^6\) Hz to the frequency ranges of the different types of electromagnetic waves. - Radio waves: < \(10^9\) Hz - Infrared waves: \(10^{12}\space \textrm{to}\space 4 \times 10^{14}\) Hz - Micro waves: \(10^9 \space \textrm{to}\space 10^{12}\) Hz - Gamma rays: > \(10^{19}\) Hz
03

Determine the category of the electromagnetic wave

Since the given frequency is \(1057 \times 10^6\) Hz, which is less than \(10^9\) Hz, it falls within the frequency range of radio waves. So, the correct answer is (A) radio waves.

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