A bulb lamp emits light of mean wavelength of `4500A`. The lamp is rated at `150W` and `8%` of the energy appears as emitted light. How many photons are emitted by the lamp per second?

Options

A. `3xx10^(19)`
B. `3xx10^(24)`
C. `3xx10^(20)`
D. `3xx10^(18)`

Explanation

To solve the problem of how many photons are emitted by the lamp per second, we can follow these steps:

### Step 1: Calculate the total energy emitted by the lamp per second.
The lamp is rated at 150 watts, and 8% of this energy is emitted as light.

\[ \text{Total Energy Emitted} = \text{Power} \times \text{Percentage of Energy Emitted} \]
\[ = 150 \, \text{W} \times 0.08 = 12 \, \text{J/s} \]

### Step 2: Convert the wavelength from angstroms to meters.
The mean wavelength of the light emitted by the lamp is given as 4500 angstroms. We need to convert this to meters for our calculations.

\[ 1 \, \text{angstrom} = 10^{-10} \, \text{meters} \]
\[ \text{Wavelength} = 4500 \, \text{angstroms} = 4500 \times 10^{-10} \, \text{m} = 4.5 \times 10^{-7} \, \text{m} \]

### Step 3: Use the energy of a single photon formula.
The energy of a single photon can be calculated using the formula:

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

Where:
- \( h = 6.626 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 4.5 \times 10^{-7} \, \text{m} \) (wavelength)

Calculating the energy of a single photon:

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{4.5 \times 10^{-7} \, \text{m}} \]

\[ E \approx \frac{1.9878 \times 10^{-25} \, \text{J m}}{4.5 \times 10^{-7} \, \text{m}} \approx 4.42 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second.
Now, we can find the number of photons emitted per second by dividing the total energy emitted by the energy of a single photon.

\[ n = \frac{\text{Total Energy Emitted}}{\text{Energy of a Single Photon}} \]
\[ n = \frac{12 \, \text{J/s}}{4.42 \times 10^{-19} \, \text{J}} \approx 2.71 \times 10^{19} \, \text{photons/s} \]

### Step 5: Round the answer.
Rounding \( 2.71 \times 10^{19} \) gives approximately \( 3 \times 10^{19} \) photons per second.

### Final Answer:
The number of photons emitted by the lamp per second is approximately \( 3 \times 10^{19} \) photons/s.

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