What is the frequency of photon, whose momentum is `1.1xx10^(-23)kgms^(-2)`

Options

A. `5xx10^(16)Hz`
B. `5xx10^(17)Hz`
C. `0.5xx10^(18)Hz`
D. `5xx10^(18)Hz`

Explanation

To find the frequency of a photon given its momentum, we can use the relationship between momentum (P), frequency (ν), and the constants involved. The steps to solve the problem are as follows:

### Step 1: Understand the relationship between momentum and frequency
The momentum of a photon can be expressed as:
\[ P = \frac{E}{c} \]
where \( E \) is the energy of the photon and \( c \) is the speed of light.

The energy of a photon can also be expressed in terms of frequency:
\[ E = h \nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency.

### Step 2: Combine the equations
From the two equations above, we can substitute \( E \) in the momentum equation:
\[ P = \frac{h \nu}{c} \]
Rearranging this gives:
\[ \nu = \frac{P c}{h} \]

### Step 3: Substitute the known values
Now we can substitute the known values into the equation:
- Given momentum \( P = 1.1 \times 10^{-23} \, \text{kg m/s} \)
- Speed of light \( c = 3 \times 10^{8} \, \text{m/s} \)
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{Js} \)

Substituting these values into the equation for frequency:
\[ \nu = \frac{(1.1 \times 10^{-23} \, \text{kg m/s}) \times (3 \times 10^{8} \, \text{m/s})}{6.626 \times 10^{-34} \, \text{Js}} \]

### Step 4: Calculate the frequency
Now we perform the calculation:
1. Calculate the numerator:
\[ 1.1 \times 10^{-23} \times 3 \times 10^{8} = 3.3 \times 10^{-15} \]

2. Now divide by Planck's constant:
\[ \nu = \frac{3.3 \times 10^{-15}}{6.626 \times 10^{-34}} \]

3. Performing the division:
\[ \nu \approx 4.98 \times 10^{18} \, \text{Hz} \]

### Step 5: Final answer
Thus, the frequency of the photon is approximately:
\[ \nu \approx 5 \times 10^{18} \, \text{Hz} \]