The dimensional formula for Planck's constant (h) is ______

Options

A. `ML^(-2)T^(-2)`
B. `ML^(2)T^(-2)`
C. `ML^(2)T^(-1)`
D. `ML^(-2)T^(-2)`

Answer

To find the dimensional formula for Planck's constant (h), we can use the relationship between energy (E), wavelength (λ), and the speed of light (c). The relevant formula is:

\[ E = \frac{h \cdot c}{\lambda} \]

### Step-by-Step Solution:

1. **Rearranging the Formula**:
Start with the formula \( E = \frac{h \cdot c}{\lambda} \). We want to isolate \( h \):
\[ h = \frac{E \cdot \lambda}{c} \]

2. **Identifying Dimensions**:
- Energy (E) has the dimensional formula:
\[ [E] = M L^2 T^{-2} \]
- Wavelength (λ) has the dimensional formula:
\[ [\lambda] = L \]
- Speed of light (c) has the dimensional formula:
\[ [c] = L T^{-1} \]

3. **Substituting Dimensions**:
Substitute the dimensional formulas into the rearranged equation for \( h \):
\[ [h] = \frac{[E] \cdot [\lambda]}{[c]} = \frac{(M L^2 T^{-2}) \cdot (L)}{(L T^{-1})} \]

4. **Simplifying the Expression**:
Now simplify the expression:
- The numerator becomes:
\[ M L^2 T^{-2} \cdot L = M L^3 T^{-2} \]
- The denominator is:
\[ L T^{-1} \]
- Thus, we have:
\[ [h] = \frac{M L^3 T^{-2}}{L T^{-1}} = M L^{3-1} T^{-2 - (-1)} = M L^2 T^{-1} \]

5. **Final Dimensional Formula**:
Therefore, the dimensional formula for Planck's constant (h) is:
\[ [h] = M L^2 T^{-1} \]

### Answer:
The dimensional formula for Planck's constant (h) is \( M L^2 T^{-1} \).