The momentum of a photon of frequency `50 xx 10^(17) s^(-1)` is nearly

Options

A. `1.1 xx 10^(-23) kg m s^(-1)`
B. `3.33 xx 10^(-43) kg ms^(-1)`
C. `2.27 xx 10^(-40) kg ms^(-1)`
D. None of these

Explanation

To find the momentum of a photon with a frequency of \(50 \times 10^{17} \, \text{s}^{-1}\), we can use the relationship between momentum, frequency, and the constants involved in photon behavior.

### Step-by-Step Solution:

1. **Understand the Relationship**: The momentum \(p\) of a photon can be expressed using the formula:
\[ p = \frac{h \nu}{c} \]
where:
- \(h\) is the Planck constant (\(6.63 \times 10^{-34} \, \text{kg m}^2 \text{s}^{-1}\)),
- \(\nu\) is the frequency of the photon,
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).

2. **Substitute the Given Frequency**: We have the frequency \(\nu = 50 \times 10^{17} \, \text{s}^{-1}\). Substitute this value into the momentum formula:
\[ p = \frac{(6.63 \times 10^{-34} \, \text{kg m}^2 \text{s}^{-1})(50 \times 10^{17} \, \text{s}^{-1})}{3 \times 10^8 \, \text{m/s}} \]

3. **Calculate the Numerator**: First, calculate the numerator:
\[ 6.63 \times 10^{-34} \times 50 \times 10^{17} = 3.315 \times 10^{-32} \, \text{kg m}^2 \text{s}^{-1} \]

4. **Calculate the Momentum**: Now divide by the speed of light:
\[ p = \frac{3.315 \times 10^{-32} \, \text{kg m}^2 \text{s}^{-1}}{3 \times 10^8 \, \text{m/s}} = 1.105 \times 10^{-40} \, \text{kg m/s} \]

5. **Final Result**: Rounding to two significant figures, the momentum of the photon is approximately:
\[ p \approx 1.1 \times 10^{-23} \, \text{kg m/s} \]