A 20 W light source emits monochromatic light of wavelength 600 nm the number of photons ejected per second in the form of avogardro 's number will be

Options

A. `N_(A)`
B. `10^(-2)N_(A)`
C. `10^(-4)N_(A)`
D. `10^(-6)N_(A)`

Answer

To find the number of photons emitted per second by a 20 W light source emitting monochromatic light of wavelength 600 nm, we can follow these steps:

### Step 1: Calculate the energy of a single photon
The energy \( E \) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) (Planck's constant) = \( 6.626 \times 10^{-34} \, \text{J s} \)
- \( c \) (speed of light) = \( 3 \times 10^8 \, \text{m/s} \)
- \( \lambda \) (wavelength) = \( 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{600 \times 10^{-9} \, \text{m}} \]

### Step 2: Perform the calculation
Calculating the above expression:
\[ E = \frac{(6.626 \times 3) \times 10^{-26}}{600 \times 10^{-9}} = \frac{19.878 \times 10^{-26}}{600 \times 10^{-9}} = \frac{19.878}{600} \times 10^{-17} \approx 3.313 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the total energy emitted per second
The total power \( P \) of the light source is given as 20 W, which means it emits 20 Joules of energy per second.

### Step 4: Calculate the number of photons emitted per second
The number of photons \( N \) emitted per second can be calculated using the formula:
\[ N = \frac{P}{E} \]
Substituting the values:
\[ N = \frac{20 \, \text{J/s}}{3.313 \times 10^{-19} \, \text{J}} \approx 6.03 \times 10^{20} \, \text{photons/s} \]

### Step 5: Convert to Avogadro's number
Avogadro's number \( N_A \) is approximately \( 6.022 \times 10^{23} \). To express the number of photons in terms of Avogadro's number:
\[ \text{Number of photons in terms of } N_A = \frac{N}{N_A} = \frac{6.03 \times 10^{20}}{6.022 \times 10^{23}} \approx 10^{-3} \, N_A \]

### Final Answer
Thus, the number of photons emitted per second in terms of Avogadro's number is:
\[ 10^{-3} \, N_A \]