A) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
B) \[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
C) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-1}}\text{T }\!\!]\!\!\text{ }\]
D) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-1}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
Correct Answer: A
Solution :
Key Idea: Place the dimensions for quantities involved in the expression comprising Plancks constant. Energy of photon \[E=h\times v\] where \[h\] is Plancks constant and \[v\]the frequency. \[\Rightarrow \] \[h=\frac{E}{v}\] \[\therefore \] \[[h]=\frac{[E]}{[v]}=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[{{T}^{-1}}]}=[M{{L}^{2}}{{T}^{-1}}]\] Alternative: Unit of Plancks constant = joule \[\times \] second So, dimensions of Plancks constant \[=[M{{L}^{2}}{{T}^{-2}}][T]\] \[=[M{{L}^{2}}{{T}^{-1}}]\]
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