Why does the sky appear blue?

Hint: Earth atmosphere is made up of many particles and gases. When light hits any of these particles it scatters. The light with higher frequency scatters more. From the visible spectrum of light, blue has the highest frequency (or shorter wavelength).Therefore blue scatters more and the sky appears to be blue.

Complete step by step answer:
The change in the direction of the motion of the particle due to the collision with another particle is known as scattering. The Sunlight which falls on the earth’s surface is scattered by the atmospheric particles like gases, dust etc. The sunlight falling on the earth’s surface can be considered as an electromagnetic wave.
As the light (electromagnetic wave) enters the atmosphere, the charged particle oscillates up and down .The electrons, protons present inside the air molecules are the charged particles. The oscillating charged particle emits electromagnetic radiation at the incident frequency. This radiation is emitted over all the directions. The particles having size less than the wavelength creates a greater impact on scattering.
The blue light which has a higher frequency makes the charged particles oscillate faster. The intensity of scattered light is proportion to the square of acceleration whereas acceleration of the charged particle $a$ is directly proportional to the square of frequency. Therefore $I \propto {\nu ^4}$, where I is the intensity and $\nu $ is the frequency of light.

Additional Information:
During the time of sunset, we see the light which has scattered less. The red light which has the lowest frequency scatters less than other colors.

Note: When we look at the sky we see that color which is redirected by the atmosphere into our line of sight, Since most of the sunlight entering the atmosphere is blue , even though violet color is scattered a bit more than the blue color, the sky appears blue.