The momentum of the photon of wavelength `5000 Å` will be

Options

A. ` 1.3 xx 10^(-27) kg -m//s `
B. `1.3 xx 10^(-28) kg-m//s `
C. `4 xx 10 ^(29) kg-m//s `
D. `4 xx 10 ^(-10) kg -m//s `

Answer

To find the momentum of a photon with a wavelength of \(5000 \, \text{Å}\), we can use the formula that relates the momentum \(p\) of a photon to its wavelength \(\lambda\):

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

Where:
- \(p\) is the momentum of the photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)),
- \(\lambda\) is the wavelength of the photon.

### Step-by-Step Solution:

**Step 1: Convert the wavelength from angstroms to meters.**
\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5.0 \times 10^{-7} \, \text{m} \]

**Step 2: Substitute the values into the momentum formula.**
\[ p = \frac{h}{\lambda} = \frac{6.626 \times 10^{-34} \, \text{J s}}{5.0 \times 10^{-7} \, \text{m}} \]

**Step 3: Perform the calculation.**
\[ p = \frac{6.626 \times 10^{-34}}{5.0 \times 10^{-7}} = 1.3252 \times 10^{-27} \, \text{kg m/s} \]

**Step 4: Round the result to two significant figures.**
\[ p \approx 1.3 \times 10^{-27} \, \text{kg m/s} \]

Thus, the momentum of the photon of wavelength \(5000 \, \text{Å}\) is approximately \(1.3 \times 10^{-27} \, \text{kg m/s}\).

### Final Answer:
The momentum of the photon is \(1.3 \times 10^{-27} \, \text{kg m/s}\).

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