According to Quantum theory of radiation, the energy $E$ of a photon of frequency $v$ is given by $E = h v$ where $h$ is Planck's constant. The dimensional formula for $h$ is:-

[M^{1} L^{2} T^{- 2}]

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[M^{1} L^{2} T^{- 1}]

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[M^{1} L^{2} T^{1}]

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[M^{1} L^{2} T^{2}]

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Solution

The correct option is B $[M^{1} L^{2} T^{- 1}]$
Since Energy of a photon, $R = h v$
$h = \frac{E}{v}$
Now, dimensional formulas of Energy,
$E = [M L^{2} T^{- 2}]$
Frequency, $V = [T^{- 1}]$
Thud, dimensional formula of Plank's constant, $h = [M L^{2} T^{- 2}] [T^{- 1}] = [M L^{2} T^{- 1}]$
Now,by its conventional definition, Angular momentum, $L = m v r$ ,
We know,
Dimensional formulas of
$\begin{matrix} m = [M^{1}] v = [L T^{- 1}] r = [L^{1}] \end{matrix}$
Thus, dimensional formula of Angular momentum, $, L [M^{1}] [L T^{- 1}] [L^{1}] = [M L^{2} T^{- 1}]$

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Find the dimensions of Planck's Constant 'h' from the equation E=hv where E is the energy and v is the frequency

Find the dimensions of Planck's constant h from the equation E = hv where E is the energy and v is the frequency.

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