## Related questions with answers

Choose the best answer to given of the following. Explain your reasoning with one or more complete sentence.

Compared to red light, blue light has higher frequency and

(a) higher energy and shorter wavelength.

(b) higher energy and longer wavelength.

(c) lower energy and shorter wavelength.

Solutions

Verified### The answer is under c):

Blue light has lower energy and a shorter wavelength compared to red light. The wavelengths of blue light are around $470$ nanometers, while red light is around $670$ nm. By knowing this, the only logical answer remains under c).

In this problem, we will see the connection between the energy, frequency, and wavelength of an electromagnetic wave (light).

The relation that connects the **frequency** $f$ and **wavelength** $\lambda$ of a photon (an eletromagnetic wave) is

$\begin{equation} \begin{split} c&=f\cdot\lambda\\ f&=\dfrac{c}{\lambda}\\ \end{split} \end{equation}$

where $c$ is the speed of light in a vacuum, the constant.

**The energy** of a single photon (quantum of light) can be obtained using Plank's equation

$\begin{equation} E=h\cdot f=h\cdot\dfrac{c}{\lambda} \end{equation}$

where $E$ is the photon's energy, $h$ is Planck's constant.

**The energy of light** in the electromagnetic spectrum increases as we increase its frequency or decrease its wavelength, as we can see in the equation $(2)$.

Looking at these two relations above, it should not be that hard to connect the dots and get to the correct answer.

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