A `200 W` sodium street lamp emits, yellow light of wavelength `0.6 mu m`. Assuming it to be `25 %` efficient in converting electric energy to light, the númber of photons of yellow light it emits per second is `n times 10^(20)`. Find n.

Answer

To solve the problem step by step, we need to calculate the number of photons emitted per second by the sodium street lamp.

### Step 1: Calculate the effective power output of the lamp
The lamp has a total power output of 200 W, and it is 25% efficient in converting electrical energy to light.

\[ \text{Effective Power (P)} = \text{Total Power} \times \text{Efficiency} = 200 \, \text{W} \times 0.25 = 50 \, \text{W} \]

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

\[ E = \frac{hc}{\lambda} \]

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

Substituting the values:

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

Calculating \( E \):

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

### Step 3: Calculate the number of photons emitted per second
The number of photons emitted per second can be calculated using the formula:

\[ n = \frac{P}{E} \]

Substituting the values we found:

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

### Step 4: Express \( n \) in the required form
The problem states that the number of photons emitted per second is \( n \times 10^{20} \). From our calculation:

\[ n \approx 1.51 \]

Thus, the value of \( n \) is approximately \( 1.5 \).

### Final Answer
The value of \( n \) is \( 1.5 \).

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