The dimensions of `h/(2pi)` will be equivalent to that of?

Options

A. momentum
B. angular momentum
C. energy
D. velocity

Answer

To determine the dimensions of \( \frac{h}{2\pi} \) and its equivalence to other physical quantities, we can follow these steps:

### Step 1: Identify the dimensions of \( h \)
Planck's constant \( h \) has dimensions of action, which can be expressed as:
\[ [h] = [M L^2 T^{-1}] \]
where:
- \( M \) is mass,
- \( L \) is length,
- \( T \) is time.

### Step 2: Analyze the term \( \frac{h}{2\pi} \)
Since \( 2\pi \) is a dimensionless constant, it does not affect the dimensions of \( h \). Therefore, the dimensions of \( \frac{h}{2\pi} \) are the same as those of \( h \):
\[ \left[\frac{h}{2\pi}\right] = [h] = [M L^2 T^{-1}] \]

### Step 3: Compare with other physical quantities
Now, we need to compare the dimensions of \( \frac{h}{2\pi} \) with the dimensions of momentum, angular momentum, energy, and velocity.

1. **Momentum \( p \)**:
\[ [p] = [M L T^{-1}] \]

2. **Angular Momentum \( L \)**:
\[ [L] = [M L^2 T^{-1}] \]

3. **Energy \( E \)**:
\[ [E] = [M L^2 T^{-2}] \]

4. **Velocity \( v \)**:
\[ [v] = [L T^{-1}] \]

### Step 4: Conclusion
From the comparison, we see that the dimensions of \( \frac{h}{2\pi} \) are equivalent to the dimensions of angular momentum \( [M L^2 T^{-1}] \).

Thus, the answer is:
\[ \frac{h}{2\pi} \text{ is equivalent to angular momentum.} \]

### Final Answer
The dimensions of \( \frac{h}{2\pi} \) will be equivalent to that of angular momentum.

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