As per de Broglie's formula, a macroscopic particle of mass 100 g and moving at a velocity of `100 cm s^(-1)` will have a wavelength of

Options

A. `6.6 xx 10^(-29) cm`
B. `6.6 xx 10^(-30) cm`
C. `6.6 xx 10^(-31) cm`
D. `6.6 xx 10^(-32) cm`

Explanation

To solve the problem of finding the wavelength of a macroscopic particle using de Broglie's formula, we can follow these steps:

### Step-by-Step Solution:

1. **Understand de Broglie's Formula**:
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle.

2. **Identify Given Values**:
- Mass of the particle (m) = 100 g
- Velocity of the particle (v) = 100 cm/s

3. **Convert Mass to Kilograms**:
Since the SI unit of mass is kilograms, we convert grams to kilograms:
\[ m = 100 \, \text{g} = \frac{100}{1000} \, \text{kg} = 0.1 \, \text{kg} \]

4. **Convert Velocity to Meters per Second**:
Similarly, we convert cm/s to m/s:
\[ v = 100 \, \text{cm/s} = \frac{100}{100} \, \text{m/s} = 1 \, \text{m/s} \]

5. **Calculate Momentum (p)**:
Momentum is given by the product of mass and velocity:
\[ p = mv = 0.1 \, \text{kg} \times 1 \, \text{m/s} = 0.1 \, \text{kg m/s} \]

6. **Use Planck's Constant**:
The value of Planck's constant \( h \) is approximately:
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]

7. **Calculate the Wavelength (λ)**:
Substitute the values of \( h \) and \( p \) into the de Broglie formula:
\[ \lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34} \, \text{Js}}{0.1 \, \text{kg m/s}} = 6.626 \times 10^{-33} \, \text{m} \]

8. **Convert Wavelength to Centimeters**:
To express the wavelength in centimeters, we convert meters to centimeters:
\[ \lambda = 6.626 \times 10^{-33} \, \text{m} = 6.626 \times 10^{-31} \, \text{cm} \]

### Final Answer:
The wavelength of the macroscopic particle is:
\[ \lambda \approx 6.626 \times 10^{-33} \, \text{m} \text{ or } 6.626 \times 10^{-31} \, \text{cm} \]