A) \[[M{{L}^{2}}{{T}^{-1}}]\]
B) \[[ML{{T}^{-2}}]\]
C) \[[M{{L}^{-2}}T]\]
D) \[[M{{L}^{-1}}{{T}^{2}}]\]
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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