The momentum of an x-ray photon with `lambda = 0.5 Å` is

Options

A. `13.26xx 10^(-26) kg- m//s`
B. `1.326xx10^(-26) kg-m//g`
C. `13.26xx10^(-24) kg-m//s`
D. `13.26 xx10^(-22) kg-m//s`

Explanation

To find the momentum of an x-ray photon with a wavelength of \( \lambda = 0.5 \, \text{Å} \), we can use the formula for the momentum of a photon:

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

where:
- \( p \) is the momentum,
- \( h \) is Planck's constant, approximately \( 6.626 \times 10^{-34} \, \text{Js} \),
- \( \lambda \) is the wavelength in meters.

### Step-by-Step Solution:

1. **Convert the Wavelength to Meters**:
The given wavelength is \( \lambda = 0.5 \, \text{Å} \).
We know that \( 1 \, \text{Å} = 10^{-10} \, \text{m} \).
Therefore,
\[ \lambda = 0.5 \, \text{Å} = 0.5 \times 10^{-10} \, \text{m} = 5.0 \times 10^{-11} \, \text{m} \]

2. **Substitute the Values into the Momentum Formula**:
Now we can substitute the values of \( h \) and \( \lambda \) into the momentum formula:
\[ p = \frac{6.626 \times 10^{-34} \, \text{Js}}{5.0 \times 10^{-11} \, \text{m}} \]

3. **Calculate the Momentum**:
Performing the division:
\[ p = \frac{6.626 \times 10^{-34}}{5.0 \times 10^{-11}} = 1.3252 \times 10^{-23} \, \text{kg m/s} \]

Rounding this to three significant figures gives:
\[ p \approx 1.33 \times 10^{-23} \, \text{kg m/s} \]

4. **Convert to the Correct Format**:
To express this in a more standard scientific notation, we can write:
\[ p \approx 13.26 \times 10^{-24} \, \text{kg m/s} \]

5. **Identify the Correct Option**:
From the options given, the closest match is:
\[ 13.26 \times 10^{-24} \, \text{kg m/s} \]
This corresponds to option 3.

### Final Answer:
The momentum of the x-ray photon is \( 13.26 \times 10^{-24} \, \text{kg m/s} \).

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