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STD 11 - 1. units,dimensions and measurement — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 1. units,dimensions and measurement4 Marks
Question
The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be
✓

Answer

$\frac{ x ^{2}}{\alpha kT } \rightarrow$ dimensionless

$\Rightarrow[\alpha]=\frac{\left[ x ^{2}\right]}{[ kT ]}=\frac{ L ^{2}}{ ML ^{2} T ^{-2}}= M ^{-1} T ^{2}$

Now $[ W ]=[\alpha][\beta]^{2}$

$[\beta]=\sqrt{\frac{ ML ^{2} T ^{-2}}{ M ^{-1} T ^{2}}}= M ^{1} L ^{1} T ^{-2}$

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