A) \[\left[ {{\text{M}}^{0}}\text{ }{{\text{L}}^{\text{0}}}\text{ }{{\text{T}}^{\text{0}}} \right]~~~~\]
B) \[\left[ {{\text{M}}^{0}}\text{ }{{\text{L}}^{\text{0}}}\text{ }{{\text{T}}^{-1}} \right]~~~~\]
C) \[\left[ {{\text{M}}^{0}}\text{ }{{\text{L}}^{\text{0}}}\text{ T} \right]~~~~\]
D) \[\left[ \text{M }{{\text{L}}^{\text{0}}}\text{ }{{\text{T}}^{-1}} \right]~~~~\]
Correct Answer: B
Solution :
\[N={{N}_{0e}}^{-\lambda t}\] Exponents are always dimensionless. So, dimensions of \[\lambda t=\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]\] \[[\lambda ][T]=[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] \[[\lambda ]\frac{[{{M}^{0}}{{L}^{0}}{{T}^{0}}]}{[T]}\] \[=[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]
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