Calculate the momentum of a particle which has de Broglie wavelength of 0.1 nm.

Options

A. `3.2 xx10^(-24) kg ms^(-1)`
B. `4.3xx 10^(-22) kg ms^(-1)`
C. `5.3xx10 ^(-22) kg ms^(-1)`
D. `6.62xx10^(-24) kg ms^(-1)`

Answer

To calculate the momentum of a particle with a de Broglie wavelength of 0.1 nm, we can follow these steps:

### Step 1: Understand the de Broglie wavelength formula
The de Broglie wavelength (\( \lambda \)) is related to the momentum (\( p \)) of a particle by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant.

### Step 2: Rearrange the formula to find momentum
We can rearrange the formula to solve for momentum:
\[ p = \frac{h}{\lambda} \]

### Step 3: Substitute the values
We know:
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{kg m}^2/\text{s} \)
- The de Broglie wavelength \( \lambda = 0.1 \, \text{nm} = 0.1 \times 10^{-9} \, \text{m} = 1.0 \times 10^{-10} \, \text{m} \)

Now, substitute these values into the momentum formula:
\[ p = \frac{6.626 \times 10^{-34}}{1.0 \times 10^{-10}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ p = 6.626 \times 10^{-34} \div 1.0 \times 10^{-10} = 6.626 \times 10^{-24} \, \text{kg m/s} \]

### Step 5: Write the final answer
Thus, the momentum of the particle is:
\[ p = 6.626 \times 10^{-24} \, \text{kg m/s} \]