The momentum of a photon is p. the corresponding wavelength is

Options

A. `h/p`
B. ph
C. `h/p^2`
D. `h/sqrtp`

Explanation

To find the corresponding wavelength of a photon given its momentum \( p \), we can use the relationship between momentum, wavelength, and Planck's constant. Here’s the step-by-step solution:

### Step 1: Understand the relationship between energy, momentum, and wavelength
The energy \( E \) of a photon can be expressed in two ways:
1. \( E = h \nu \) (where \( h \) is Planck's constant and \( \nu \) is the frequency)
2. \( E = pc \) (where \( p \) is the momentum and \( c \) is the speed of light)

### Step 2: Relate frequency and wavelength
The frequency \( \nu \) is related to the wavelength \( \lambda \) by the equation:
\[ \nu = \frac{c}{\lambda} \]

### Step 3: Substitute frequency into the energy equation
Substituting \( \nu \) into the energy equation gives:
\[ E = h \left(\frac{c}{\lambda}\right) \]
Thus, we can write:
\[ E = \frac{hc}{\lambda} \]

### Step 4: Set the two expressions for energy equal
Since both expressions represent the energy of the same photon, we can set them equal:
\[ pc = \frac{hc}{\lambda} \]

### Step 5: Solve for wavelength
To find the wavelength \( \lambda \), we can rearrange the equation:
\[ \lambda = \frac{hc}{p} \]

### Step 6: Express the final result
Now, we can express the wavelength in terms of momentum:
\[ \lambda = \frac{h}{p} \]

### Conclusion
Thus, the corresponding wavelength \( \lambda \) of a photon with momentum \( p \) is given by:
\[ \lambda = \frac{h}{p} \]

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