The de Broglie wave length associated with a particle of mass 1 mg moving with a velocity of 1m/sec is

Options

A. `6.63 xx 10^(-29)m`
B. `6.63 xx 10^(-31) m`
C. `6.63 xx 10^(-28)m`
D. `6.63 xx 10^(-22) m`

Answer

To find the de Broglie wavelength associated with a particle of mass 1 mg moving with a velocity of 1 m/s, we can follow these steps:

### Step 1: Understand the formula for de Broglie wavelength
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( h \) is the Planck constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( m \) is the mass of the particle in kilograms,
- \( v \) is the velocity of the particle in meters per second.

### Step 2: Convert the mass from milligrams to kilograms
The mass given is 1 mg. To convert this to kilograms:
\[ 1 \, \text{mg} = 1 \times 10^{-3} \, \text{g} = 1 \times 10^{-6} \, \text{kg} \]

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the de Broglie wavelength formula. We have:
- \( h = 6.626 \times 10^{-34} \, \text{Js} \)
- \( m = 1 \times 10^{-6} \, \text{kg} \)
- \( v = 1 \, \text{m/s} \)

Substituting these values into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{(1 \times 10^{-6})(1)} = \frac{6.626 \times 10^{-34}}{1 \times 10^{-6}} \]

### Step 4: Calculate the wavelength
Perform the division:
\[ \lambda = 6.626 \times 10^{-34} \times 10^{6} = 6.626 \times 10^{-28} \, \text{m} \]

### Step 5: Final answer
Thus, the de Broglie wavelength associated with the particle is:
\[ \lambda = 6.626 \times 10^{-28} \, \text{m} \]