Problem 2166 - JEE Physics

Question

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

Step-by-Step Solution

Answer

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 1: 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

Step 2: 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

Step 3: 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.

Key Concepts

Frequency Conversion

Frequency conversion is a process used to express a frequency in different units. Normally, we measure frequency in hertz (Hz), but for ease of use, larger or smaller units like megahertz (MHz) or gigahertz (GHz) are often utilized. To convert MHz to Hz, multiply the number by \(10^6\), since 1 MHz is equivalent to 1,000,000 Hz. Therefore, a frequency of 1057 MHz can be expressed as \(1057 \times 10^6\) Hz. Similarly, converting from other units, like GHz to Hz, involves multiplying by \(10^9\). Frequency conversion helps us compare frequencies within the electromagnetic spectrum by using a common unit.

Radio Waves

Radio waves are a type of electromagnetic wave with frequencies ranging from under 1 Hz up to \(10^9\) Hz. These waves are one of the longest wavelengths in the electromagnetic spectrum. Radio waves are commonly used for communication. Many everyday applications, such as AM and FM radio, TV broadcasting, and wireless networks, utilize these frequencies. They are excellent for these applications because they can travel long distances and penetrate through buildings and other obstacles. The low energy and long wavelength of radio waves make them safe and effective for many practical uses.

Electromagnetic Waves Classification

Electromagnetic waves are classified based on their frequency and wavelength, which determine their energy. The electromagnetic spectrum includes several types of waves, such as:

• Radio Waves: Frequencies up to \(10^9\) Hz.
• Microwaves: Frequencies from \(10^9\) to \(10^{12}\) Hz.
• Infrared Waves: Frequencies from \(10^{12}\) to \(4 \times 10^{14}\) Hz.
• Visible Light: Frequencies from \(4 \times 10^{14}\) to \(8 \times 10^{14}\) Hz.
• Ultraviolet Light: Frequencies from \(8 \times 10^{14}\) to \(10^{17}\) Hz.
• X-Rays: Frequencies from \(10^{17}\) to \(10^{19}\) Hz.
• Gamma Rays: Frequencies above \(10^{19}\) Hz.

The classification is crucial because it informs us about the characteristics and potential uses of each type of wave, from communication and heating to medical imaging and radiation therapy.