A modern 200 W sodium street lamp emits yellow light of wavelength 0.6 `mum`. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is

Options

A. `1.5xx10^(20)`
B. `6xx10^(18)`
C. `62xx10^(20)`
D. `3xx10^(19)`

Answer

To solve the problem, we need to calculate the number of photons emitted by a sodium street lamp per second, given its power and efficiency. Here’s a step-by-step solution:

### Step 1: Calculate the Power Converted to Light
The lamp has a total power of 200 W and is 25% efficient in converting electrical energy to light.

\[ P_{light} = \text{Efficiency} \times P_{total} \]

Substituting the values:

\[ P_{light} = 0.25 \times 200 \, \text{W} = 50 \, \text{W} \]

### Step 2: Calculate the Energy of a Single Photon
The energy of a photon can be calculated using the formula:

\[ E_{photon} = \frac{hc}{\lambda} \]

Where:
- \( h = 6.626 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 0.6 \, \mu m = 0.6 \times 10^{-6} \, \text{m} \)

Substituting the values:

\[ E_{photon} = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{0.6 \times 10^{-6} \, \text{m}} \]

Calculating this gives:

\[ E_{photon} = \frac{1.9878 \times 10^{-25}}{0.6 \times 10^{-6}} \approx 3.313 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the Number of Photons Emitted per Second
Now, we can find the number of photons emitted per second using the formula:

\[ n = \frac{P_{light}}{E_{photon}} \]

Substituting the values:

\[ n = \frac{50 \, \text{W}}{3.313 \times 10^{-19} \, \text{J}} \approx 1.51 \times 10^{20} \, \text{photons/s} \]

### Final Answer
The number of photons emitted by the sodium street lamp per second is approximately:

\[ n \approx 1.5 \times 10^{20} \, \text{photons/s} \]