If the energy of a photon is 10 eV , then its momentum is

Options

A. ` 5.33xx 10^(-23) kg-m//s `
B. ` 5.33 xx 10^(-25) kg - m//s `
C. `5.33 xx 10^(-29) kg-m//s `
D. `5.33 xx 10^(-27) kg -m//s `

Answer

To find the momentum of a photon given its energy, we can use the relationship between energy and momentum for photons. Here’s a step-by-step solution:

### Step 1: Understand the relationship between energy and momentum
The energy (E) of a photon is related to its momentum (p) by the equation:
\[ E = pc \]
where \( c \) is the speed of light.

### Step 2: Rearrange the equation to find momentum
From the equation \( E = pc \), we can rearrange it to find momentum:
\[ p = \frac{E}{c} \]

### Step 3: Convert the energy from eV to joules
The energy is given as 10 eV. We need to convert this to joules. The conversion factor is:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ joules} \]
So,
\[ E = 10 \text{ eV} = 10 \times 1.6 \times 10^{-19} \text{ J} = 1.6 \times 10^{-18} \text{ J} \]

### Step 4: Use the speed of light
The speed of light \( c \) is approximately:
\[ c = 3 \times 10^8 \text{ m/s} \]

### Step 5: Substitute the values into the momentum equation
Now we can substitute the values of \( E \) and \( c \) into the momentum equation:
\[ p = \frac{E}{c} = \frac{1.6 \times 10^{-18} \text{ J}}{3 \times 10^8 \text{ m/s}} \]

### Step 6: Calculate the momentum
Now, performing the calculation:
\[ p = \frac{1.6 \times 10^{-18}}{3 \times 10^8} \]
\[ p = \frac{1.6}{3} \times 10^{-18} \times 10^{-8} \]
\[ p = 0.5333 \times 10^{-26} \text{ kg m/s} \]
\[ p \approx 5.33 \times 10^{-27} \text{ kg m/s} \]

### Step 7: Final answer
Thus, the momentum of the photon is:
\[ p \approx 5.33 \times 10^{-27} \text{ kg m/s} \]