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

Options

A. `6.63 xx 10^-33`
B. `6.63 xx 10^-34 m`
C. `6.63 xx 10^-35 m`
D. `6.65 xx 10^-35 m`

Explanation

To find the de-Broglie wavelength of a particle with a mass of 1 gram and a velocity of 100 m/s, we can use the de-Broglie wavelength formula:

\[ \lambda = \frac{h}{mv} \]

where:
- \(\lambda\) is the de-Broglie wavelength,
- \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{J s}\)),
- \(m\) is the mass of the particle in kilograms,
- \(v\) is the velocity of the particle in meters per second.

### Step 1: Convert mass from grams to kilograms
Given mass = 1 g, we convert it to kilograms:
\[ m = 1 \, \text{g} = 1 \times 10^{-3} \, \text{kg} \]

### Step 2: Substitute the values into the de-Broglie wavelength formula
Now we can substitute \(h\), \(m\), and \(v\) into the formula:
\[ \lambda = \frac{6.63 \times 10^{-34} \, \text{J s}}{(1 \times 10^{-3} \, \text{kg})(100 \, \text{m/s})} \]

### Step 3: Calculate the denominator
Calculate the product of mass and velocity:
\[ mv = (1 \times 10^{-3} \, \text{kg})(100 \, \text{m/s}) = 1 \times 10^{-1} \, \text{kg m/s} = 0.1 \, \text{kg m/s} \]

### Step 4: Calculate the de-Broglie wavelength
Now substitute back into the equation:
\[ \lambda = \frac{6.63 \times 10^{-34}}{0.1} = 6.63 \times 10^{-33} \, \text{m} \]

### Final Answer
The de-Broglie wavelength of the particle is:
\[ \lambda = 6.63 \times 10^{-33} \, \text{meters} \]