A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb.

Options

A. `3xx10^(20)s^(-1)`
B. `2xx10^(-20)s^(-1)`
C. `2xx10^(20)s^(-1)`
D. `1xx10^(-20)s^(-1)`

Explanation

To solve the problem of calculating the number of photons emitted per second by a 100-watt bulb that emits monochromatic light of wavelength 400 nm, we can follow these steps:

### Step 1: Understand the given data
- Power of the bulb (P) = 100 watts = 100 joules/second
- Wavelength of light (λ) = 400 nm = 400 × 10^(-9) meters

### Step 2: Calculate the energy of one photon
The energy (E) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) = Planck's constant = \( 6.626 \times 10^{-34} \) joule seconds
- \( c \) = speed of light = \( 3 \times 10^{8} \) meters/second
- \( \lambda \) = wavelength in meters

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{400 \times 10^{-9} \, \text{m}} \]

### Step 3: Perform the calculation
Calculating the numerator:
\[ 6.626 \times 10^{-34} \times 3 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]
Now, divide by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25}}{400 \times 10^{-9}} = \frac{1.9878 \times 10^{-25}}{4 \times 10^{-7}} = 4.9695 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second
The number of photons emitted per second (N) can be calculated using the formula:
\[ N = \frac{P}{E} \]
Substituting the values:
\[ N = \frac{100 \, \text{J/s}}{4.9695 \times 10^{-19} \, \text{J}} \]

### Step 5: Perform the final calculation
Calculating the number of photons:
\[ N = \frac{100}{4.9695 \times 10^{-19}} \approx 2.01 \times 10^{20} \, \text{photons/s} \]

### Final Answer
The number of photons emitted per second by the bulb is approximately \( 2 \times 10^{20} \) photons/s.

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