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Units and Measurement

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Physics Part I

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Physics

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Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase : 970 kg m–3. Are the two densities of the same order of magnitude ? If so, why?

Diameter space of space sodium space atom space is space equal space to space the space size space of space sodium space atom.

That space is space straight D space equals space 2.5 space straight Å space

So comma space radius space of space sodium space atom comma space straight r space equals space left parenthesis 1 divided by 2 right parenthesis space cross times space 2.5 space straight Å space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1.25 space straight Å space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1.25 space cross times space 10 to the power of negative 10 end exponent space straight m space

Volume space of space sodium space atom comma space straight V space equals space 4 over 3 πr cubed space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 4 over 3 cross times 3.14 cross times left parenthesis 1.25 cross times 10 to the power of negative 10 end exponent right parenthesis cubed space
According space to space the space Avogadro space hypothesis comma
one space mole space of space sodium space contains space 6.023 space cross times space 10 to the power of 23 space atoms space
and space has space straight a space mass space of space 23 space straight g space or space 23 space cross times space 10 to the power of – 3 end exponent space kg.

therefore space space Mass space of space one space atom space equals space fraction numerator space 23 space cross times space 10 to the power of – 3 end exponent space over denominator space 6.023 space cross times space 10 to the power of 23 end fraction space equals space straight m subscript 1 space

Density space of space sodium space atom comma space straight rho space equals space straight m subscript 1 over straight V space

Putting space values space in space this space equation comma space

Density space of space sodium space atom comma space straight rho space equals 4.67 space cross times space 10 to the power of negative 3 end exponent space Kg space straight m to the power of negative 3 end exponent space

Density space of space sodium space in space crystalline space phase space equals space 970 space kg space straight m to the power of negative 3 end exponent space
Hence, the density of sodium atom and the density of sodium in its crystalline phase are not in the same order. This is because in solid phase, atoms are closely packed. Thus, the inter-atomic separation is very small in the crystalline phase. 
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What is measurement?

Measurement is the process of attaching a numeric value to an aspect of a natural phenomenon. Measurement is making the quantitative knowledge of a physical quantity. 
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What is the need of measurement?

To get the complete knowledge of any physical quantity, measurement is needed. Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. Knowledge without measurement is incomplete and unsatisfactory. 
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Give four examples of physical quantities.

Examples of Physical quantitie are force, mass, density and power.
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Define unit.

The quantity used as a standard of measurement is called unit. 

Example: Unit of time is second. 

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Define physical quantity.

 


A measurable quantity in terms of which laws of Physics can be expressed is called physical quantity.

The result of a measurement of a physical quantity is expressed by a number accompanied by a unit.


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