What is the wavelength of matter waves associated with a paticle of mass 200 gm and moving with a velocity of 100 m/s?

Options

A. `6.6xx10^(-33) m`
B. `3.3 xx 10^(-35) m`
C. `2.2 xx10^(-34) m`
D. `5.4 xx10^(-34) m`

Explanation

To find the wavelength of matter waves associated with a particle, we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant, and
- \(p\) is the momentum of the particle.

### Step 1: Convert the mass to kilograms
The mass of the particle is given as 200 grams. We need to convert this to kilograms because the standard unit of mass in physics is kilograms.

\[ \text{Mass} = 200 \, \text{g} = \frac{200}{1000} \, \text{kg} = 0.2 \, \text{kg} \]

### Step 2: Calculate the momentum
Momentum \(p\) is given by the product of mass and velocity:

\[ p = m \cdot v \]

Substituting the values:

\[ p = 0.2 \, \text{kg} \cdot 100 \, \text{m/s} = 20 \, \text{kg m/s} \]

### Step 3: Use Planck's constant
Planck's constant \(h\) is approximately:

\[ h = 6.626 \times 10^{-34} \, \text{Js} \]

### Step 4: Calculate the de Broglie wavelength
Now, we can substitute the values of \(h\) and \(p\) into the de Broglie wavelength formula:

\[ \lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34} \, \text{Js}}{20 \, \text{kg m/s}} \]

Calculating this gives:

\[ \lambda = \frac{6.626 \times 10^{-34}}{20} = 3.313 \times 10^{-35} \, \text{m} \]

### Final Answer
The wavelength of the matter waves associated with the particle is:

\[ \lambda = 3.313 \times 10^{-35} \, \text{m} \]

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