A photon of energy 3.3 eV , find the momentum of photon is

Options

A. `1.76 xx 10^(-23)kg-m//s`
B. `1.76 xx 10^(-27)kg-m//s`
C. `1.76 xx 10^(-25)kg-m//s`
D. `1.76 xx 10^(-30)kg-m//s`

Answer

To find the momentum of a photon with an energy of 3.3 eV, we can follow these steps:

### Step 1: Understand the relationship between energy and momentum of a photon
The energy (E) of a photon is related to its momentum (P) by the equation:
\[ E = P \cdot c \]
where \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s).

### Step 2: Convert the energy from electron volts to joules
Since the energy is given in electron volts (eV), we need to convert it to joules. The conversion factor is:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ joules} \]
Thus, for 3.3 eV:
\[ E = 3.3 \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} \]
Calculating this gives:
\[ E = 5.28 \times 10^{-19} \text{ J} \]

### Step 3: Rearrange the energy-momentum equation to find momentum
From the equation \( E = P \cdot c \), we can rearrange it to solve for momentum:
\[ P = \frac{E}{c} \]

### Step 4: Substitute the values into the momentum equation
Now, substituting the values we have:
\[ P = \frac{5.28 \times 10^{-19} \text{ J}}{3 \times 10^8 \text{ m/s}} \]

### Step 5: Perform the calculation
Now we can perform the calculation:
\[ P = \frac{5.28 \times 10^{-19}}{3 \times 10^8} \]
\[ P = 1.76 \times 10^{-27} \text{ kg m/s} \]

### Final Answer
The momentum of the photon is:
\[ P = 1.76 \times 10^{-27} \text{ kg m/s} \]

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