The momentum of photon of frequency `10^9 Hz` will be

Options

A. `31Kg m//s`
B. `7.3 xx 10^(-29) Kg m//s`
C. `2.2 xx 10^(-33) kg - m//s `
D. `6.6 xx 10^(-26) kg - m//s `

Answer

To find the momentum of a photon with a frequency of \(10^9 \, \text{Hz}\), we can use the relationship between momentum, frequency, and Planck's constant. Here’s a step-by-step solution:

### Step 1: Understand the relationship between momentum and frequency
The momentum \(p\) of a photon can be expressed using the formula:
\[ p = \frac{h \cdot f}{c} \]
where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(f\) is the frequency of the photon,
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).

### Step 2: Substitute the known values
Given:
- Frequency \(f = 10^9 \, \text{Hz}\),
- Planck's constant \(h = 6.626 \times 10^{-34} \, \text{Js}\),
- Speed of light \(c = 3 \times 10^8 \, \text{m/s}\).

We can substitute these values into the momentum formula:
\[ p = \frac{(6.626 \times 10^{-34} \, \text{Js}) \cdot (10^9 \, \text{Hz})}{3 \times 10^8 \, \text{m/s}} \]

### Step 3: Calculate the momentum
Now, we will perform the calculation:
\[ p = \frac{6.626 \times 10^{-34} \cdot 10^9}{3 \times 10^8} \]
Calculating the numerator:
\[ 6.626 \times 10^{-34} \cdot 10^9 = 6.626 \times 10^{-25} \, \text{Js} \]

Now, divide by the speed of light:
\[ p = \frac{6.626 \times 10^{-25}}{3 \times 10^8} = 2.20867 \times 10^{-33} \, \text{kg m/s} \]

Rounding this to two significant figures gives:
\[ p \approx 2.2 \times 10^{-33} \, \text{kg m/s} \]

### Final Answer
The momentum of the photon with a frequency of \(10^9 \, \text{Hz}\) is approximately:
\[ \boxed{2.2 \times 10^{-33} \, \text{kg m/s}} \]

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