Question

Compared to red light, blue light has (A) a higher frequency and a shorter wavelength and carries more energy (B) a lower frequency and a longer wavelength and carries more energy (C) a lower frequency and a longer wavelength and carries less energy (D) a higher frequency and a shorter wavelength and carries less energy

Short answer

Compared to red light, blue light has a higher frequency and shorter wavelength, meaning it carries more energy. So, the correct answer is (A).

Step-by-step solution

1. Relationship between speed, frequency, and wavelength in light waves

Light waves are electromagnetic waves, and they travel at the speed of light (c). The relationship between the speed of light (c), frequency (f) and wavelength (λ) is given by the formula: \[c = f \cdot λ\] We must remember that: - Higher frequency means a shorter wavelength - Lower frequency means a longer wavelength

2. Relationship between energy and frequency in light waves

The energy (E) of light is directly proportional to its frequency (f) and can be described using Planck's constant (h): \[E = h \cdot f\] Thus, higher frequency carries more energy, while lower frequency carries less energy.

3. Comparing red light and blue light

Now let's compare red light and blue light using the relationships in steps 1 and 2: - Red light has a longer wavelength and a lower frequency than blue light. - Therefore, red light carries less energy than blue light.

4. Choose the correct option

Based on the comparisons made in step 3, we can now choose the correct option: (A) Blue light has a higher frequency and a shorter wavelength and carries more energy. So the correct answer is (A).

Key concepts

Relationship Between Light Wavelength and Frequency

The nature of light as an electromagnetic wave can be fascinating, and it follows some fundamental rules that can help us understand a lot about its behavior. One of these rules involves the relationship between the light's wavelength and frequency. The speed of light is consistent at approximately 299,792 kilometers per second in a vacuum. This speed (\( c \) ) is the product of the light's wavelength (\( \text{\textgreek{λ}} \) ) and frequency (\( f \) ), articulated through the equation \begin{align*} c = f \times \text{\textgreek{λ}}ewline ewline \end{align*}.

• If we have a high frequency, the light wave vibrates more quickly, and as a result, its wavelength will be shorter.
• Conversely, a lower frequency means the light wave vibrates less often, leading to a longer wavelength.

This relationship is crucial in understanding why different colors of light behave the way they do. For example, blue light has a shorter wavelength and, therefore, a higher frequency compared to red light, which has a longer wavelength and lower frequency.

Energy and Frequency of Light Waves

Another aspect of light that is key to understand its effects is how its energy relates to frequency. This might seem a bit abstract, but think of light as packets of energy called photons. The energy (\( E \) ) carried by each photon is directly proportional to its frequency (\( f \)), connected through Planck's constant (\( h \) ), known from the world-changing work of Max Planck.\begin{align*} E = h \times fewline ewline \end{align*}.

• Light with higher frequency, like ultraviolet light, carries more energy per photon.
• The reverse is true for light with lower frequency, such as infrared light, which carries less energy per photon.

It means high-frequency light doesn't just appear different but is fundamentally more energetic at a particle level. This is why ultraviolet light can cause sunburn – its high energy affects the skin cells more than the lower energy light like red or infrared.

Understanding Electromagnetic Waves

The term 'electromagnetic waves' might sound complex, but it's just the scientific way of referring to light in all its forms, visible and invisible. These waves comprise a vast spectrum, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, each with its own unique properties. They all share the characteristic of being able to travel through a vacuum, like outer space, at the speed of light.

Characteristics of Electromagnetic Waves

• They do not need a medium to travel, unlike sound waves that require air.
• They are transverse waves, meaning their oscillations are perpendicular to the direction of wave propagation.
• Electromagnetic waves can exhibit both wave-like and particle-like properties, a concept known as wave-particle duality.

The implications of electromagnetic waves are vast, affecting technology, medicine, and even our daily life. From the microwave that heats your food to the colors you distinguish with your eyes, they all relate back to this broad and fundamental concept of electromagnetic waves.