The number of photons emitted by a 60 W bulb per second, if 10% of the electrical energy supplied to an incandescent light bulb is radiated as visible light, is

Options

A. `1.8xx10^19`
B. `1.8xx10^16`
C. `1.8xx10^11`
D. `1.8xx10^21`

Answer

To solve the problem of calculating the number of photons emitted by a 60 W bulb per second, given that 10% of the electrical energy is radiated as visible light, we can follow these steps:

### Step 1: Determine the total energy radiated as visible light per second
Since the bulb has a power of 60 W, it radiates 60 joules of energy per second. However, only 10% of this energy is emitted as visible light.

\[ \text{Energy radiated as visible light} = 10\% \times 60 \, \text{J} = 0.10 \times 60 \, \text{J} = 6 \, \text{J} \]

### Step 2: Calculate the energy of a single photon
We will use the formula for the energy of a photon:

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

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 of visible light) = 5600 Å = \( 5600 \times 10^{-10} \, \text{m} \)

Now substituting the values into the formula:

\[ E = \frac{(6.63 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{5600 \times 10^{-10} \, \text{m}} \]

Calculating this gives:

\[ E \approx 3.616 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the number of photons emitted per second
Now, we can find the number of photons emitted per second by dividing the total energy radiated as visible light by the energy of a single photon.

\[ \text{Number of photons} = \frac{\text{Total energy radiated}}{\text{Energy of one photon}} = \frac{6 \, \text{J}}{3.616 \times 10^{-19} \, \text{J}} \]

Calculating this gives:

\[ \text{Number of photons} \approx 1.66 \times 10^{19} \]

### Final Answer
The number of photons emitted by the 60 W bulb per second is approximately \( 1.66 \times 10^{19} \).