If a photon has velocity c and frequency v , then which of the following represents its wavelength ?

Options

A. ` (hv)/(c^(2))`
B. `hv `
C. `(hc)/(v)`
D. `(c)/(v)`

Answer

To find the wavelength of a photon given its velocity \( c \) and frequency \( v \), we can use the relationship between these quantities. Here’s a step-by-step solution:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The speed of light \( c \) is related to frequency \( v \) and wavelength \( \lambda \) by the equation:
\[ c = v \cdot \lambda \]

### Step 2: Rearrange the equation to find the wavelength
To find the wavelength \( \lambda \), we can rearrange the equation:
\[ \lambda = \frac{c}{v} \]

### Step 3: Substitute the known values
In this case, we know that the speed of light \( c \) is a constant (approximately \( 3 \times 10^8 \) m/s) and \( v \) is the frequency of the photon. Thus, we can express the wavelength in terms of the frequency:
\[ \lambda = \frac{c}{v} \]

### Step 4: Conclusion
The wavelength of the photon can be represented as:
\[ \lambda = \frac{c}{v} \]

Therefore, the correct representation of the wavelength of a photon in terms of its velocity and frequency is \( \frac{c}{v} \).

### Final Answer
The wavelength \( \lambda \) is given by:
\[ \lambda = \frac{c}{v} \]

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