The units for equation `lambda = (h)/(mv)` are

Options

A. `(kg m^(2) s^(-1))/(kg ms^(-1))`
B. `(kg m s^(-1))/(ms^(-1))`
C. `(kg^(2) m^(2) s^(-2))/(kg m^(2)s^(-1))`
D. `(kg^(2) m s^(-3))/(kg m)`

Answer

To determine the units for the equation \( \lambda = \frac{h}{mv} \), we will analyze the units of each component in the equation step by step.

### Step 1: Identify the components of the equation
The equation consists of:
- \( \lambda \): Wavelength
- \( h \): Planck's constant
- \( m \): Mass
- \( v \): Velocity

### Step 2: Write down the units for each component
1. **Wavelength (\( \lambda \))**: The unit of wavelength is typically meters (m).
2. **Planck's constant (\( h \))**: The unit of Planck's constant is \( \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1} \).
3. **Mass (\( m \))**: The unit of mass is kilograms (kg).
4. **Velocity (\( v \))**: The unit of velocity is meters per second (m/s).

### Step 3: Substitute the units into the equation
The equation can be rewritten in terms of units:
\[ \lambda = \frac{h}{mv} \]
Substituting the units, we get:
\[ \text{Units of } \lambda = \frac{\text{Units of } h}{\text{Units of } m \cdot \text{Units of } v} \]
This becomes:
\[ \text{Units of } \lambda = \frac{\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1}}{\text{kg} \cdot \left(\text{m/s}\right)} \]

### Step 4: Simplify the units
Now, we simplify the right-hand side:
\[ \text{Units of } \lambda = \frac{\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1}}{\text{kg} \cdot \left(\frac{\text{m}}{\text{s}}\right)} = \frac{\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1}}{\text{kg} \cdot \text{m} \cdot \text{s}^{-1}} \]
The kg cancels out, and we are left with:
\[ \text{Units of } \lambda = \frac{\text{m}^2}{\text{m}} = \text{m} \]

### Step 5: Conclusion
The unit of \( \lambda \) is meters (m), which is consistent with the physical interpretation of wavelength.

### Final Answer
The units for the equation \( \lambda = \frac{h}{mv} \) are meters (m).

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