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. `1.4` x `10^(18)`
B. `1.4` x `10^(20)`
C. `1.4` x `10^(19)`
D. `1.4` x `10^(21)`

Answer

To solve the problem, we need to calculate the number of photons emitted by the bulb per second. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the total power emitted as light
The bulb has a power rating of 200 W, but only 10% of this power is emitted as light.

\[ \text{Power emitted as light} = 200 \, \text{W} \times 0.10 = 20 \, \text{W} \]

### Step 2: Convert power to energy per second
Since 1 W = 1 J/s, the energy emitted as light per second is:

\[ \text{Energy emitted per second} = 20 \, \text{J/s} \]

### 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:
- \( h = 6.63 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 1400 \, \text{Å} = 1400 \times 10^{-10} \, \text{m} \)

Now substituting the values:

\[ E = \frac{(6.63 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{1400 \times 10^{-10} \, \text{m}} \]

Calculating the numerator:

\[ E = \frac{(6.63 \times 3) \times 10^{-34 + 8}}{1400 \times 10^{-10}} = \frac{19.89 \times 10^{-26}}{1400 \times 10^{-10}} = \frac{19.89}{1400} \times 10^{-16} \]

Calculating further:

\[ E \approx 1.42 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second
Now we can find the number of photons emitted per second using the formula:

\[ \text{Number of photons} = \frac{\text{Total energy emitted per second}}{\text{Energy of one photon}} \]

Substituting the values:

\[ \text{Number of photons} = \frac{20 \, \text{J}}{1.42 \times 10^{-19} \, \text{J}} \approx 1.41 \times 10^{20} \]

### Final Answer
The number of photons emitted by the bulb per second is approximately \( 1.41 \times 10^{20} \).

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