The momentum of a photon is `33 xx 10^(- 29) kg - m//sec`. Its frequency will be

Options

A. `3 xx 10^(3) Hz`
B. `6 xx 10^(3) Hz`
C. `7.5 xx 10^(12) Hz`
D. `1.5 xx 10^(13) Hz`

Explanation

To find the frequency of a photon given its momentum, we can use the relationship between momentum, wavelength, and frequency. Here is a step-by-step solution:

### Step 1: Understand the relationship between momentum, wavelength, and frequency
The momentum \( p \) of a photon is given by the formula:
\[ p = \frac{h}{\lambda} \]
where \( h \) is Planck's constant and \( \lambda \) is the wavelength of the photon.

### Step 2: Rearrange the formula to find wavelength
From the above formula, we can express wavelength \( \lambda \) as:
\[ \lambda = \frac{h}{p} \]

### Step 3: Substitute values into the equation
We know:
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{Js} \)
- Momentum \( p = 33 \times 10^{-29} \, \text{kg m/s} \)

Substituting these values into the wavelength formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{33 \times 10^{-29}} \]

### Step 4: Calculate the wavelength
Calculating the above expression:
\[ \lambda = \frac{6.626}{33} \times 10^{-34 + 29} = \frac{6.626}{33} \times 10^{-5} \approx 0.2008 \times 10^{-5} \, \text{m} = 2.008 \times 10^{-6} \, \text{m} \]

### Step 5: Use the wavelength to find frequency
The frequency \( f \) of the photon is related to its wavelength by the equation:
\[ f = \frac{c}{\lambda} \]
where \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step 6: Substitute the wavelength into the frequency formula
Substituting the value of \( \lambda \):
\[ f = \frac{3 \times 10^8}{2.008 \times 10^{-6}} \]

### Step 7: Calculate the frequency
Calculating the above expression:
\[ f \approx 1.493 \times 10^{14} \, \text{Hz} \]

### Final Answer
The frequency of the photon is approximately:
\[ f \approx 1.5 \times 10^{14} \, \text{Hz} \]

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