Question

Planck's constant has the dimensions

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

Answer 1

The correct option is D

$\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$

1. Planck's constant relates the energy of a photon to its corresponding frequency using the formula, $\mathrm{E}=h\nu$ where, $E$ is the energy, $h$is Planck's constant,$\nu$ is frequency.
2. The S.I unit of Planck's constant is $J.s$
3. The Dimension of energy $\mathrm{E}$ is $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$.
4. Dimension of frequency $\mathrm{v}$ is $\left[{\mathrm{T}}^{-1}\right]$.
5. Hence the dimension of Planck's constant $h$ is $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$.

Hence, option D is the correct answer.