The de-Broglie wavelength of a particle with mass `1 g` and velocity `100 m//sec` is.

Options

A. `6.63 xx10^(-33) m`
B. `6.63xx10^(-34) m`
C. `6.63xx10^(-35)m`
D. `6.65xx10^(-36)m`

Explanation

To find the de-Broglie wavelength of a particle with a mass of 1 g and a velocity of 100 m/s, we can follow these steps:

### Step 1: Understand the de-Broglie Wavelength Formula
The de-Broglie wavelength (\( \lambda \)) is given by the formula:
\[ \lambda = \frac{h}{p} \]
where:
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \, \text{Js} \))
- \( p \) is the momentum of the particle.

### Step 2: Calculate the Momentum
The momentum (\( p \)) of a particle is calculated using the formula:
\[ p = m \cdot v \]
where:
- \( m \) is the mass of the particle in kilograms (kg)
- \( v \) is the velocity of the particle in meters per second (m/s)

Given:
- Mass \( m = 1 \, \text{g} = 1 \times 10^{-3} \, \text{kg} \)
- Velocity \( v = 100 \, \text{m/s} \)

Now, substituting the values:
\[ p = (1 \times 10^{-3} \, \text{kg}) \cdot (100 \, \text{m/s}) = 1 \times 10^{-1} \, \text{kg m/s} \]

### Step 3: Substitute Values into the de-Broglie Wavelength Formula
Now, we substitute \( p \) into the de-Broglie wavelength formula:
\[ \lambda = \frac{h}{p} = \frac{6.63 \times 10^{-34} \, \text{Js}}{1 \times 10^{-1} \, \text{kg m/s}} \]

### Step 4: Perform the Calculation
Calculating \( \lambda \):
\[ \lambda = \frac{6.63 \times 10^{-34}}{1 \times 10^{-1}} = 6.63 \times 10^{-33} \, \text{m} \]

### Step 5: Conclusion
The de-Broglie wavelength of the particle is:
\[ \lambda = 6.63 \times 10^{-33} \, \text{m} \]