A 100 watt bulb radiates 15% of energy given in the form of visible light . If wavelength of the visible photons are nearly `5,000Å` , then calculate the number of visible light photons emitted per second.

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total power emitted as visible light
The bulb has a power rating of 100 watts, and it radiates 15% of its energy as visible light.

\[ \text{Power emitted as visible light} = 100 \, \text{W} \times 0.15 = 15 \, \text{W} \]

### Step 2: Convert the power emitted to energy per second
Since power is defined as energy per unit time, the energy emitted as visible light per second is equal to the power emitted.

\[ \text{Energy emitted per second} = 15 \, \text{J/s} \]

### Step 3: 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) = \( 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \)

Now substituting the values:

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{5 \times 10^{-7} \, \text{m}} \]

Calculating the energy:

\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{5 \times 10^{-7} \, \text{m}} = 3.9756 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second
To find the number of photons emitted per second, we divide the total energy emitted per second by the energy of a single photon:

\[ \text{Number of photons} = \frac{\text{Energy emitted per second}}{\text{Energy of a single photon}} = \frac{15 \, \text{J}}{3.9756 \times 10^{-19} \, \text{J}} \]

Calculating the number of photons:

\[ \text{Number of photons} \approx 3.77 \times 10^{20} \]

### Final Answer
The number of visible light photons emitted per second by the 100 watt bulb is approximately \( 3.77 \times 10^{20} \).

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