The energy E of a photon and its frequency u are expressed by the… - Vidyadip

Question

The energy E of a photon and its frequency u are expressed by the relation E = hv. State the dimensions and unit of Planck's constant h.

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Answer

According to question,
$\begin{aligned}E & =h u
\\\text { Dimension of } h & =\frac{\text { Dimension of } E}{\text { Dimension of } v}\end{aligned}$
$\text { Dimension of energy } E=\left[M^1 L^2 T^{-2}\right]$
Dimension of frequency $v=\left[ T ^{-1}\right]$
$\therefore$ Dimension of Planck's constant $h$
$\begin{array}{l}
=\left[\frac{ML^2 T^{-2}}{T^{-1}}\right] \\
=\left[M^1 L^2 T^{-1}\right]\end{array}$

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