If wavelength of photon is 3×`10 ^(−11)` m, h=6.6×`10 ^(−34)`Jsec, then momentum of photon is

Options

A. `2.2×10^(−23)kgms^(−1)`
B. `6×10^(−23)kgms^(−1)`
C. `4×10^(−23)kgms^(−1)`
D. `5×10^(−23)kgms^(−1)`

Answer

To find the momentum of a photon given its wavelength and Planck's constant, we can follow these steps:

### Step 1: Identify the given values
- Wavelength of the photon (λ) = \(3 \times 10^{-11}\) m
- Planck's constant (h) = \(6.6 \times 10^{-34}\) J·s

### Step 2: Use the de Broglie wavelength equation
The momentum (p) of a photon can be calculated using the de Broglie wavelength equation:
\[ \lambda = \frac{h}{p} \]
From this equation, we can rearrange it to solve for momentum:
\[ p = \frac{h}{\lambda} \]

### Step 3: Substitute the values into the equation
Now, we substitute the given values of h and λ into the equation:
\[ p = \frac{6.6 \times 10^{-34} \text{ J·s}}{3 \times 10^{-11} \text{ m}} \]

### Step 4: Perform the calculation
Now, we can perform the division:
\[ p = \frac{6.6}{3} \times \frac{10^{-34}}{10^{-11}} = 2.2 \times 10^{-23} \text{ kg·m/s} \]

### Step 5: Write the final answer
The momentum of the photon is:
\[ p = 2.2 \times 10^{-23} \text{ kg·m/s} \]