Planck's constant has dimension $\underline{\hspace{2.5cm}}$,

Step 1: Identify the relation for Planck's constant.

Planck's constant $h$ relates the energy of a photon $E$ to its frequency $\nu$.

$$E = h\nu$$

Rearranging the formula gives the dimension of $h$ in terms of energy and frequency.

$$[h] = \frac{[E]}{[\nu]}$$

Step 2: Determine the dimensions of energy.

Energy has the same dimensions as work, which is force multiplied by distance.

$$[E] = [F \cdot d]$$ $$[E] = [MLT^{-2}] \cdot [L]$$ $$[E] = [ML^{2}T^{-2}]$$

Step 3: Determine the dimensions of frequency.

Frequency is the reciprocal of the time period.

$$[\nu] = [T^{-1}]$$

Step 4: Calculate the dimension of Planck's constant.

Substitute the dimensions of energy and frequency back into the rearranged formula.

$$[h] = \frac{[ML^{2}T^{-2}]}{[T^{-1}]}$$ $$[h] = [ML^{2}T^{-1}]$$

Step 5: Verify using the de Broglie relation.

We can cross-check this result using the de Broglie wavelength equation, where $p$ is momentum and $\lambda$ is wavelength.

$$\lambda = \frac{h}{p}$$ $$[h] = [p][\lambda]$$ $$[h] = [MLT^{-1}][L]$$ $$[h] = [ML^{2}T^{-1}]$$

Both methods yield the same dimensional formula.

Answer: $[ML^{2}T^{-1}]$