Momentum of photon of energy 3 ke V in kg - m/s will be

Options

A. `1.6 xx 10^(-19)`
B. `1.6 xx 10^(-21)`
C. `1.6 xx 10^(-24)`
D. `1.6 xx 10^(-27)`

Explanation

To find the momentum of a photon with an energy of 3 keV, 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 of a photon
The momentum \( p \) of a photon can be calculated using the formula:
\[ p = \frac{E}{c} \]
where \( E \) is the energy of the photon and \( c \) is the speed of light in a vacuum.

### Step 2: Convert the energy from keV to joules
The energy given is 3 keV (kilo-electron volts). We need to convert this energy into joules. We know that:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ joules} \]
Thus,
\[ 3 \text{ keV} = 3 \times 10^3 \text{ eV} = 3 \times 10^3 \times 1.6 \times 10^{-19} \text{ joules} \]
Calculating this gives:
\[ E = 3 \times 1.6 \times 10^{-16} \text{ joules} = 4.8 \times 10^{-16} \text{ joules} \]

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

### Step 4: Calculate the momentum
Now, substituting the values of \( E \) and \( c \) into the momentum formula:
\[ p = \frac{E}{c} = \frac{4.8 \times 10^{-16} \text{ joules}}{3 \times 10^8 \text{ m/s}} \]
Calculating this gives:
\[ p = \frac{4.8}{3} \times 10^{-16} \times 10^{-8} \text{ kg m/s} = 1.6 \times 10^{-24} \text{ kg m/s} \]

### Final Answer
The momentum of the photon of energy 3 keV is:
\[ p = 1.6 \times 10^{-24} \text{ kg m/s} \]