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One atmosphere is numerically equal to approximately:
A.${{10}^{6}}\,dyne\,c{{m}^{-2}}$
B.${{10}^{2}}\,dyne\,c{{m}^{-2}}$
C.${{10}^{4}}\,dyne\,c{{m}^{-2}}$
D.${{10}^{8}}\,dyne\,c{{m}^{-2}}$


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Last updated date: 21st Jun 2024
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Answer
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Hint: The concept of the standard convention of SI units is to be used here. There are certain rules, for example multiplication, or division that need to be performed so that the conversion of units takes place.

Complete step by step solution:
In order to answer our question, we need to know about the International System of Units(SI). The CGPM is one of the intergovernmental treaty organizations created by a diplomatic treaty known as Meter Convention which was signed in Paris in 1875. SI system is a modification of a metric system and has seven base units pertaining to the seven fundamental scientific quantities. The definition of SI base units are given below:

Unit of lengthMetreThe metre is the length of the distance or path that is travelled by light in vacuum during a time interval of $\dfrac{1}{299792458}$of a second.
Unit of massKilogramThe kilogram is the standard unit which represents mass; it is equal to the mass of the international prototype of the kilogram.
Unit of timeSecondThe second is the duration of 9 192 631 770 periods that corresponds to the transition between the 2 hyperfine levels of the ground state of the caesium-133 atom radiation.
Unit of electric currentAmpereThe ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, would produce a force equal to $2\times {{10}^{-7}}$ newton per metre of length between these conductors and placed 1 metre apart in vacuum.
Unit of thermodynamic temperatureKelvinThe kelvin, unit of thermodynamic temperature, is the fraction $\dfrac{1}{273.16}$ of the thermodynamic temperature of the triple point of water
Unit of amount of substanceMole1. The mole can be defined as the quantity of substance of a system whichcontains exact quantity as there are atoms in0.012 kilogram of carbon-12; its symbol is "mol".2. When the term mole is used, then the constituent substances or particles must be specified and may be atoms, molecules, ions, electrons or something else.
Unit of luminous intensitycandelaThe candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540\times {{10}^{12}}$ hertz and that has a radiant intensity in that direction of $\dfrac{1}{683}$ watt per steradian.

Now, let us come to our question. One atmosphere is numerically equal to 101,325 pascals, or newtons per square metre. So, we can convert it to $dyne\,c{{m}^{-2}}$as:
\[{{P}_{dyne\,c{{m}^{-2}}}}={{P}_{atm}}\times 1.01325\times {{10}^{6}},but\,{{P}_{atm}}=1\]

So,${{P}_{dyne\,c{{m}^{-2}}}}={{10}^{-6}}dyne\,c{{m}^{-2}}$. Hence, we get option A as our correct answer.

NOTE: There are some physical quantities which are derived using the SI base units in combinations e.g.. metre square (${{m}^{2}}$) is the unit for area, the cubic metre (${{m}^{3}}$) is the unit for volume and $kg\,{{m}^{-3}}$ is unit of density. Such units are called derived units.