Question

the energy of a photon depends upon its frequency. find the dimensions of the coeff. of the frequency(planck's constant) by the method of dimensions?

Answer 1

$$\begin{gathered} Energyofthephotonisgivenby: \\ E=h\nu \\ wherehistheplank\text{'}scons\tan t \\ Dimensionofenergy=\left[M{L}^2{T}^{-2}\right] \\ dimensionoffrequency\left(\nu \right)=\left[T^{-1}\right] \\ \left[M{L}^2{T}^{-2}\right]=h\left[T^{-1}\right] \\ h=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[T^{-1}\right]}=\left[M{L}^2{T}^{-1}\right] \end{gathered}$$