Question

What is the wavelength of a photon of red light (in nm) whose frequency is 4.56 × 1014 hz?

Answer 1

To calculate the wavelength of the light, we use the relation between wavelength, speed of light and frequency as

$\lambda =\frac{c}{f}$

Here, $\lambda$ is the wavelength of the light , $f$ is the frequency of the light $c$ is the speed of light.

Given $f=4.56\times10^{14}  Hz$ and $c=3\times 10^{8} m/s$

Substituting these values in above relation, we get

$\lambda =\frac{10^{8} m/s}{4.56\times10^{14}} m$

$\lambda = 6.578\times10^{-7} m$

In nano meter,

$\lambda = 657.89 \times 10^{-9} m=657.89 nm$

Thus, the wavelength of photon of the red light is 657.89 nm.

Answer 2

The wavelength of the photon of the red light will be $\boxed{658\text{ nm}}$.

Explanation:

The photon of a particular light exhibits the wave length and it has a particular wavelength and frequency as it moves in the medium.

The wavelength of a wave is defined as the distance between the two successive crests or troughs of a wave's motion whereas the frequency of the wave is defined as the number of cycles completed by the wave in time period of $1\text{ s}$.

All the light waves are the electromagnetic waves and therefore, they travel at the speed of light. The speed of light in the air is $3\times10^{8}\text{ m/s}$.

Write the expression for the wavelength of the photon of red light.

$\boxed{\lambda=\dfrac{c}{f}}$

Here, $\lambda$ is the wavelength of the photon, $c$ is the speed of light and $f$ is the frequency of oscillation of photon.

Substitute the values in above expression.

$\begin{aligned}\lambda&=\dfrac{3\times10^{8}}{4.56\times10^{14}}\text{ m}\\&=6.58\times10^{-7}\text{ m}\\&=658\text{ nm}\end{aligned}$

Thus, The wavelength of the photon of the red light will be $\boxed{658\text{ nm}}$.

Learn More:

1. Conservation of energy brainly.com/question/3943029

2. Charge on a capacitor brainly.com/question/8892837  

3. Energy levels brainly.com/question/6054540

Answer Details:

Grade: Middle School

Subject: Physics

Chapter: Photons

Keywords:

wavelength, photon, red light, frequency, cycles, oscillations, crests, successive, troughs, electromagnetic, speed of light.