If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare? how will their accelerations compare? their directions of travel?

The forces (magnitude) would be the same; the electron would have a larger acceleration, and they will travel in opposite directions

Explanation:

- The magnitude of the force exerted on a charged particle by an electric field is

where q is the magnitude of the charge and E is the electric field strength. Since the proton and the electron have same electric charge magnitude (e, elementary charge), they will experience the same force under the same electric field.

- The acceleration of a particle is given by

where F is the force exerted on the particle and m is the mass. Here, we said that the electron and the proton experience the same force F, however the mass of the proton is much larger (approx. 1800 times larger) than the mass of the electron, so the electron will experience a larger acceleration (because acceleration is inversely proportional to the mass)

- The direction of travel corresponds to the direction of the force. Since the proton is positively charged, the force exerted on it has same direction as the electric field; while since the electron is negatively charged, the force exerted on it has opposite direction to the electric field. Therefore, the two particles will travel into opposite directions.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

wavelength divides in half and speed stays the same.