Question

The dimensional formula of Planck’s constant is

• A. $\left[\right.ML^{- 3}T^{- 1}\left]\right.$
• B. $\left[\right.ML^{- 2}T^{- 1}\left]\right.$
• C. $\left[\right.M^{0}L^{- 1}T^{- 3}\left]\right.$
• D. $\left[\right.ML^{2}T^{- 1}\left]\right.$

Answer 1

Answer: (D)

According to Planck:
$E = h v$
$h = \frac{E}{v}$
Substituting the dimensions of known physical quantities:
$ \, \, \, \left[\right. h \left]\right.=\frac{\left[\right. M L^{2} T^{ - 2} \left]\right.}{\left[\right. T^{ - 1} \left]\right.} \\ or \, \, \left[\right. h \left]\right.=ML^{2}T^{ - 1}$
So, SI unit or Planck’s constant is kg m²s^-1 which can also be written as
$\left(\right. k g \, \, m^{2} \, s^{ - 2} \left.\right) \times s$ . But as $k g \, \, m^{2} \, s^{ - 2}$ is joule, so unit of h is $j o u l e \, \, \times \, \, sec$ , i.e., Js.