A) \[\left[ M{{L}^{2}}{{T}^{-2}} \right]\,and\,\left[ ML{{T}^{-1}} \right]\]
B) \[\left[ M{{L}^{2}}{{T}^{-1}} \right]\,and\,\left[ M{{L}^{2}}{{T}^{-1}} \right]\]
C) \[\left[ M{{L}^{2}}{{T}^{1}} \right]\,and\,\left[ M{{L}^{2}}{{T}^{-2}} \right]\]
D) \[\left[ ML{{T}^{-1}} \right]\,and\,\left[ ML{{T}^{-2}} \right]\]
Correct Answer: B
Solution :
Key Idea: Find two relations in which Planck's Constant and angular momentum exist and then put dimensions or other physical quantities. We Know that \[E=hv\] Where h is Planck's constant, v is frequency. \[\therefore \] \[h=\frac{E}{v}\] \[\therefore \] \[\left[ h \right]=\frac{\left[ M{{L}^{2}}{{T}^{2}} \right]}{\left[ {{T}^{-1}} \right]}=\left[ M{{L}^{2}}{{T}^{-1}} \right]\] Angular momentum=momentum \[\times \]distance \[=\left[ ML{{T}^{-1}} \right]\,\,\left[ L \right]\] \[=\left[ M{{L}^{2}}{{T}^{-1}} \right]\] Note: Planck?s constant and angular momentum both have the same dimensions.
You need to login to perform this action.
You will be redirected in
3 sec
