If 5% of the energy supplied to a bulb is irradiated as visible light, how many quanta are emitted per second by a 100 W lamp? (Assume, wavelength of visible light as `5.6xx10^(-5)cm`)

Options

A. `1.4xx10^(19)`
B. `3xx10^(3)`
C. `1.4xx10^(-19)`
D. `3xx10^(4)`

Explanation

To solve the problem of how many quanta are emitted per second by a 100 W lamp that irradiates 5% of its energy as visible light, we can follow these steps:

### Step 1: Calculate the energy emitted as visible light per second
The total power of the bulb is 100 W, and 5% of this power is emitted as visible light.

\[ \text{Energy emitted as visible light} = 5\% \times 100 \text{ W} = \frac{5}{100} \times 100 = 5 \text{ J/s} \]

### Step 2: Determine the wavelength in meters
The wavelength of visible light is given as \(5.6 \times 10^{-5} \text{ cm}\). We need to convert this to meters.

\[ \text{Wavelength} (\lambda) = 5.6 \times 10^{-5} \text{ cm} = 5.6 \times 10^{-7} \text{ m} \]

### Step 3: Use the energy of a single 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) = \(3 \times 10^{8} \text{ m/s}\)

### Step 4: Calculate the energy of a single photon
Substituting the values into the formula:

\[ E = \frac{(6.63 \times 10^{-34} \text{ J s}) \times (3 \times 10^{8} \text{ m/s})}{5.6 \times 10^{-7} \text{ m}} \]

Calculating this gives:

\[ E = \frac{1.989 \times 10^{-25} \text{ J m}}{5.6 \times 10^{-7} \text{ m}} \approx 3.55 \times 10^{-19} \text{ J} \]

### Step 5: Calculate the number of photons emitted per second
Now, we can find the number of photons emitted per second (\(n\)) by dividing the total energy emitted per second by the energy of a single photon:

\[ n = \frac{\text{Total energy emitted per second}}{\text{Energy of a single photon}} = \frac{5 \text{ J/s}}{3.55 \times 10^{-19} \text{ J}} \approx 1.41 \times 10^{19} \]

### Final Answer
Thus, the number of quanta (photons) emitted per second by the 100 W lamp is approximately:

\[ n \approx 1.41 \times 10^{19} \text{ photons/s} \]

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