The momentum of photon of electromagnetic radiation is `3.3xx10^(-29)kgms^-1`. What is the frequency and wavelength of the waves associated with it ? `h=6.6xx10^(-34)Js`.

Options

A. `1.5 xx 10^(13)` Hz
B. `7.5 xx 10^(12) Hz`
C. `6.0 xx 10^(13) Hz`
D. `3.0 xx 10^(3) Hz`

Answer

To find the frequency and wavelength of the electromagnetic radiation associated with a photon of momentum \( p = 3.3 \times 10^{-29} \, \text{kg m/s} \) and Planck's constant \( h = 6.6 \times 10^{-34} \, \text{Js} \), we can follow these steps:

### Step 1: Use the relationship between momentum and wavelength
The momentum \( p \) of a photon is related to its wavelength \( \lambda \) by the equation:
\[ p = \frac{h}{\lambda} \]
Rearranging this equation gives:
\[ \lambda = \frac{h}{p} \]

### Step 2: Substitute the values of \( h \) and \( p \)
Substituting the given values into the equation:
\[ \lambda = \frac{6.6 \times 10^{-34} \, \text{Js}}{3.3 \times 10^{-29} \, \text{kg m/s}} \]

### Step 3: Calculate the wavelength
Calculating the wavelength:
\[ \lambda = \frac{6.6}{3.3} \times 10^{-34 + 29} = 2 \times 10^{-5} \, \text{m} \]

### Step 4: Use the speed of light to find frequency
The frequency \( \nu \) of the electromagnetic wave is related to its wavelength \( \lambda \) by the equation:
\[ c = \lambda \nu \]
Where \( c \) is the speed of light (\( c \approx 3 \times 10^8 \, \text{m/s} \)). Rearranging gives:
\[ \nu = \frac{c}{\lambda} \]

### Step 5: Substitute the values of \( c \) and \( \lambda \)
Substituting the values:
\[ \nu = \frac{3 \times 10^8 \, \text{m/s}}{2 \times 10^{-5} \, \text{m}} \]

### Step 6: Calculate the frequency
Calculating the frequency:
\[ \nu = \frac{3}{2} \times 10^{8 + 5} = 1.5 \times 10^{13} \, \text{Hz} \]

### Final Results
- The frequency \( \nu \) of the electromagnetic radiation is \( 1.5 \times 10^{13} \, \text{Hz} \).
- The wavelength \( \lambda \) is \( 2 \times 10^{-5} \, \text{m} \).