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Why is air pressure greatest at the earth’s surface?

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Answer
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Hint: Atmospheric pressure or air pressure is also known as barometric pressure. Atmospheric pressure simply defines the pressure exerted within the atmosphere around our earth. Atmospheric pressure is measured at two places: at sea level and another one is at surface level.

Complete Step By Step Answer:
Atmospheric pressure which is calculated with reference to the pressure over the sea level is known as sea level pressure. Atmospheric pressure which is calculated with reference to the pressure over the surface level is known as surface pressure of a particular location.
As we know earth has its own gravitational field which is spread all around the earth surface, originating from the core of the earth. The gravitation field of earth is a function of length between the core and the point in the atmosphere. Hence, as we move away from the core of the earth the strength of the gravitational force decreases gradually. Because of this reason, the strength of gravitational pull or force is maximum at the surface of the earth where we live.
Our atmosphere is made up of different types of gases which form a layer around the earth surface. These gaseous particles are in a random motion and therefore exert some pressure over the earth surface. The strength of air pressure is maximum at the earth's surface because due to higher strength of gravitational pull large numbers of atmospheric gases come closer to each other and form a denser layer, so due to formation of this denser layer the air pressure increases over the earth surface.
As we move away from the earth surface amount as well as composition of gases changes with change in gravitational pull and hence the air pressure also decreases.

Note:
As we move above from the sea level air pressure decreases and its value reaches ${\dfrac{1}{3}^{rd}}$ of its value at mount Everest. As the air pressure decreases the solubility of oxygen also decreases in the body and hypoxia is developed in people. Air pressure of $1$ atm is considered at the sea level.