The dimensions of the quantity `hc` (where `h=h/(2pi)`) is

Options

A. `[ML^(2)T^(-1)]`
B. `[MLT^(-1)]`
C. `[ML^(3)T^(-2)]`
D. `[ML^(3)T^(-1)]`

Answer

To find the dimensions of the quantity \( hc \), where \( h = \frac{h}{2\pi} \), we first need to understand what \( h \) represents. In physics, \( h \) typically refers to Planck's constant, which has dimensions of energy multiplied by time.

1. **Identify the dimensions of Planck's constant \( h \)**:
- The dimensions of energy (E) are given by \( [E] = [M][L^2][T^{-2}] \).
- Since \( h \) is energy multiplied by time, we have:
\[ [h] = [E][T] = [M][L^2][T^{-2}][T] = [M][L^2][T^{-1}] \]

2. **Calculate the dimensions of \( c \)**:
- The speed of light \( c \) has dimensions of length per time:
\[ [c] = [L][T^{-1}] \]

3. **Combine the dimensions of \( h \) and \( c \)**:
- Now, we find the dimensions of the product \( hc \):
\[ [hc] = [h][c] = [M][L^2][T^{-1}][L][T^{-1}] \]
- Simplifying this, we get:
\[ [hc] = [M][L^2][L][T^{-1}][T^{-1}] = [M][L^3][T^{-2}] \]

4. **Final result**:
- Therefore, the dimensions of \( hc \) are:
\[ [hc] = [M][L^3][T^{-2}] \]

Thus, the dimensions of the quantity \( hc \) are \( M L^3 T^{-2} \).