Energy of a photon is 20 eV then its momentum is

Options

A. ` 5.33 xx 10 ^( -27)` kg - m/sec
B. `10.66 xx 10 ^(-25) ` kg - m/sec
C. ` 10 .66 xx 10 ^(-27)` kg-m/sec
D. ` 5.33 xx 10^(-30)` kg-m/sec

Answer

To find the momentum of a photon given its energy, we can follow these steps:

### Step 1: Understand the relationship between energy and momentum of a photon
The momentum \( p \) of a photon can be expressed in terms of its energy \( E \) using the formula:
\[ p = \frac{E}{c} \]
where \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step 2: Convert the energy from electron volts to joules
The energy of the photon is given as \( 20 \, \text{eV} \). To convert this energy to joules, we use the conversion factor:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Thus,
\[ E = 20 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 32 \times 10^{-19} \, \text{J} = 3.2 \times 10^{-18} \, \text{J} \]

### Step 3: Substitute the values into the momentum formula
Now, substituting the energy in joules and the speed of light into the momentum formula:
\[ p = \frac{3.2 \times 10^{-18} \, \text{J}}{3 \times 10^8 \, \text{m/s}} \]

### Step 4: Calculate the momentum
Calculating the above expression:
\[ p = \frac{3.2 \times 10^{-18}}{3 \times 10^8} = \frac{3.2}{3} \times 10^{-18} \times 10^{-8} = 1.06667 \times 10^{-26} \, \text{kg m/s} \]
Rounding this to three significant figures, we get:
\[ p \approx 1.07 \times 10^{-26} \, \text{kg m/s} \]

### Final Answer
The momentum of the photon is approximately \( 1.07 \times 10^{-26} \, \text{kg m/s} \).

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