A 200 W bulb emits monochromatic light of wavelenght 1400 A and only 10% of the energy is emitted as light. The number of photons emitted by the bulb per second will be

Options

A. `1.4xx10^(18)`
B. `1.4xx10^(20)`
C. `1.4xx10^(19)`
D. `1.4xx10^(21)`

Answer

To solve the problem of finding the number of photons emitted by a 200 W bulb that emits monochromatic light of wavelength 1400 Å, we can follow these steps:

### Step 1: Calculate the energy emitted as light
The bulb emits only 10% of its energy as light. Therefore, we first need to calculate the energy emitted as light per second.

\[ \text{Energy emitted as light} = \text{Power} \times \text{Percentage of energy emitted as light} \]
\[ = 200 \, \text{W} \times 0.10 = 20 \, \text{J/s} \]

### Step 2: Convert the wavelength from Angstroms to meters
The wavelength is given as 1400 Å. We need to convert this into meters for our calculations.

\[ 1 \, \text{Å} = 10^{-10} \, \text{m} \]
\[ \text{Wavelength in meters} = 1400 \, \text{Å} \times 10^{-10} \, \text{m/Å} = 1.4 \times 10^{-7} \, \text{m} \]

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

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

Where:
- \( h \) (Planck's constant) = \( 6.63 \times 10^{-34} \, \text{J s} \)
- \( c \) (speed of light) = \( 3 \times 10^{8} \, \text{m/s} \)
- \( \lambda \) (wavelength) = \( 1.4 \times 10^{-7} \, \text{m} \)

Substituting the values:

\[ E = \frac{(6.63 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{1.4 \times 10^{-7} \, \text{m}} \]
\[ = \frac{1.989 \times 10^{-25} \, \text{J m}}{1.4 \times 10^{-7} \, \text{m}} \approx 1.42 \times 10^{-18} \, \text{J} \]

### 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 as light by the energy of one photon.

\[ \text{Number of photons} = \frac{\text{Energy emitted as light}}{\text{Energy of one photon}} \]
\[ = \frac{20 \, \text{J/s}}{1.42 \times 10^{-18} \, \text{J}} \approx 1.41 \times 10^{19} \, \text{photons/s} \]

Thus, the number of photons emitted by the bulb per second is approximately \( 1.41 \times 10^{19} \).

### Final Answer
The number of photons emitted by the bulb per second is \( 1.41 \times 10^{19} \).

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