Animated Solution for Physics - Electromagnetic Waves: Arrange the following electromagnetic radiations per quantum in the order of increasing energy. A. Blue light B. Yellow light C. X-ray D. Radio wave

Have you ever wondered why X-rays can see through your skin, but the visible light from a bulb just bounces off? Or why radio waves can travel for miles to bring music to your car, but they don't give you a sunburn? The secret lies in the fundamental properties of electromagnetic waves: their wavelength and their energy.

In this problem, we are asked to arrange four different types of electromagnetic radiations—Blue light, Yellow light, X-rays, and Radio waves—in order of their increasing energy per quantum. Let's break this down step by step and uncover the beautiful physics behind it.

Energy of a Photon

To understand the energy of electromagnetic radiation, we need to look at it through the lens of quantum mechanics. According to Max Planck and Albert Einstein, electromagnetic radiation isn't just a continuous wave; it's made up of tiny, discrete packets of energy called quanta, or photons.

The energy $E$ of a single photon is given by the famous equation:

Here, $h$ is Planck's constant, $c$ is the speed of light in a vacuum, and $\lambda$ is the wavelength of the radiation.

Since $h$ and $c$ are both constants, this equation reveals a profound truth: Energy is inversely proportional to wavelength.

This means that if a wave has a very long wavelength, its photons carry very little energy. Conversely, if a wave has a very short wavelength, its photons are packed with high energy.

Now, let's look at the electromagnetic spectrum. The spectrum is a continuous range of all possible electromagnetic wavelengths, from the longest radio waves to the shortest gamma rays.

Let's locate our four candidates on this spectrum:

1. Radio waves (D): These are the giants of the spectrum. Their wavelengths can range from a millimeter to hundreds of kilometers! Because their wavelength is so large, their energy per photon is the lowest.

2. Visible Light (A & B): This is the narrow band of the spectrum that our eyes can detect. Within this band, we have the colors of the rainbow (VIBGYOR). Red has the longest wavelength, and violet has the shortest. Therefore, Yellow light (B) has a longer wavelength than Blue light (A).

3. X-rays (C): These are highly energetic waves with extremely short wavelengths, roughly the size of atoms. This is why they can penetrate soft tissues!

Let's arrange our radiations in order of decreasing wavelength (which corresponds to increasing energy):

- Longest wavelength: Radio wave (D) - Next: Yellow light (B) - Next: Blue light (A) - Shortest wavelength: X-ray (C)

Mathematically, we can write this as:

Because energy is inversely proportional to wavelength, the order of increasing energy is exactly the reverse:

So, the correct sequence is D, B, A, C.

This simple relationship, $E=\frac{hc}{\lambda }$, is a cornerstone of modern physics. It explains everything from why ultraviolet light causes sunburns (higher energy than visible light) to how microwave ovens heat our food. By mastering the electromagnetic spectrum, you gain a deeper understanding of how the universe interacts with matter on a microscopic level. Keep exploring, and never stop questioning!