In atomic physics, the energy E of a photon is related to its frequency f by the formula E… — JAMB UTME

In atomic physics, the energy $E$ of a photon is related to its frequency $f$ by the formula $E = h f$ , where $h$ is Planck's constant. What are the fundamental dimensions of Planck's constant $h$ ?

$M L^2 T^{-1}$ Answer
B
$M L^2 T^{-2}$
C
$M L T^{-1}$
D
$M L^2 T^{-3}$

Answer

The fundamental dimensions of Planck's constant are

M L^2 T^{-1}

Planck's constant

h

is given by

h = E / f

. Since energy

E

has fundamental dimensions of

M L^2 T^{-2}

and frequency

f

has dimensions of

T^{-1}

, dividing energy by frequency yields

\frac{M L^2 T^{-2}}{T^{-1}} = M L^2 T^{-1}

Step-by-Step Solution

Express Planck's constant in terms of energy and frequency

h = \frac{E}{f}

Rearranging the equation

E = h f

isolates

h

Determine the fundamental dimensions of energy (

E

) and frequency (

f

)

[E] = M L^2 T^{-2}

and

[f] = T^{-1}

Energy has dimensions of work (

F \times d = M L T^{-2} \cdot L = M L^2 T^{-2}

) and frequency is inverse time (

T^{-1}

Divide the dimensions of energy by the dimensions of frequency

[h] = \frac{M L^2 T^{-2}}{T^{-1}} = M L^2 T^{-2 - (-1)} = M L^2 T^{-1}

Applying the rules of indices simplifies the exponent of time.

Key Concept

Dimensional Analysis of Physical Constants

Estimated Time:1m 0s

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