Q. The dimensional formula of universal gas constant:

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A

$ \text{6}000\text{ { }\!\!\mathrm{\AA}\!\!\text{ }} $

B

$ \text{5}000\text{ { }\!\!\mathrm{\AA}\!\!\text{ }} $

C

$ \text{4000 { }\!\!\mathrm{\AA}\!\!\text{ }} $

D

none of these

Solution:

Using the relation $ R=\frac{PV}{0} $ Dimensions of gas constant R $ =\frac{\dimensions\,of\,pressure\,\times \dimensions\,of\,volume}{\dimension\,of\,temperature} $ $ =\frac{[M{{L}^{-1}}{{T}^{-2}}][{{L}^{3}}]}{\theta } $ $ =[M{{L}^{-2}}{{T}^{-2}}{{\theta }^{-1}}] $

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