An X-ray has a wavelength of 0.010 Å. Its momentum is

Options

A. `2.126xx10^(-23) kg ms^(-1)`
B. `6.626xx10^(-22) kg ms^(-1)`
C. `3.456xx10^(-25) kg ms^(-1)`
D. `3.313xx10^(-22) kg ms^(-1)`

Explanation

To find the momentum of an X-ray with a wavelength of 0.010 Å, we can follow these steps:

### Step 1: Understand the relationship between momentum and wavelength
The momentum \( P \) of a photon (or X-ray) is given by the formula:
\[ P = \frac{h}{\lambda} \]
where:
- \( P \) is the momentum,
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \, \text{Js} \)),
- \( \lambda \) is the wavelength of the photon.

### Step 2: Convert the wavelength from angstroms to meters
The given wavelength is \( 0.010 \, \text{Å} \). We need to convert this to meters:
\[ 0.010 \, \text{Å} = 0.010 \times 10^{-10} \, \text{m} = 1.0 \times 10^{-12} \, \text{m} \]

### Step 3: Substitute the values into the momentum formula
Now we can substitute the values into the momentum formula:
\[ P = \frac{h}{\lambda} = \frac{6.63 \times 10^{-34} \, \text{Js}}{1.0 \times 10^{-12} \, \text{m}} \]

### Step 4: Calculate the momentum
Now we perform the calculation:
\[ P = 6.63 \times 10^{-34} \div 1.0 \times 10^{-12} = 6.63 \times 10^{-22} \, \text{kg m/s} \]

### Step 5: Final result
Thus, the momentum of the X-ray is:
\[ P = 6.63 \times 10^{-22} \, \text{kg m/s} \]

### Conclusion
The correct option from the given choices is \( 6.626 \times 10^{-22} \, \text{kg m/s} \).

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