The de Broglie wavelength associated with a particle of mass `10^-6` kg with a velocity of `10 ms^-1` is (h=6.625 × `10^-34Js`)

Options

A. `6.626×10^-34`m
B. `6.626×10^-29`m
C. `6.626 × 10^-28` m
D. `6.626 × 10^-40`m

Answer

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

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

where:
- \(\lambda\) is the de Broglie wavelength,
- \(h\) is the Planck's constant (\(6.625 \times 10^{-34} \, \text{Js}\)),
- \(m\) is the mass of the particle,
- \(v\) is the velocity of the particle.

### Step 1: Identify the given values
- Mass of the particle, \(m = 10^{-6} \, \text{kg}\)
- Velocity of the particle, \(v = 10 \, \text{ms}^{-1}\)
- Planck's constant, \(h = 6.625 \times 10^{-34} \, \text{Js}\)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the de Broglie wavelength formula:

\[ \lambda = \frac{6.625 \times 10^{-34} \, \text{Js}}{(10^{-6} \, \text{kg})(10 \, \text{ms}^{-1})} \]

### Step 3: Calculate the denominator
First, calculate the denominator:

\[ m \cdot v = (10^{-6} \, \text{kg}) \cdot (10 \, \text{ms}^{-1}) = 10^{-5} \, \text{kg m/s} \]

### Step 4: Calculate the wavelength
Now, substitute the denominator back into the equation:

\[ \lambda = \frac{6.625 \times 10^{-34} \, \text{Js}}{10^{-5} \, \text{kg m/s}} \]

Calculating this gives:

\[ \lambda = 6.625 \times 10^{-34} \div 10^{-5} = 6.625 \times 10^{-34 + 5} = 6.625 \times 10^{-29} \, \text{m} \]

### Final Answer
The de Broglie wavelength associated with the particle is:

\[ \lambda = 6.625 \times 10^{-29} \, \text{m} \]

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