The number of photons emitted per second by a 60 W source of monochromatic light of wavelength 663 nm is:
`(h=6.63xx10^(-34)Js )`

Options

A. `4xx10^(-20)`
B. `1.5xx10^(20)`
C. `2xx10^(-20)`
D. `2xx10^(20)`

Explanation

To find the number of photons emitted per second by a 60 W source of monochromatic light with a wavelength of 663 nm, we can follow these steps:

### Step 1: Understand the relationship between power, energy, and time
The power (P) of the light source is defined as the energy (E) emitted per unit time (t):
\[ P = \frac{E}{t} \]
This means that the energy emitted per second is equal to the power of the source.

### Step 2: 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:
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the light in meters.

First, convert the wavelength from nanometers to meters:
\[ \lambda = 663 \, \text{nm} = 663 \times 10^{-9} \, \text{m} \]

Now, substitute the values into the energy formula:
\[ E = \frac{(6.63 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{663 \times 10^{-9} \, \text{m}} \]

### Step 3: Calculate the energy of a single photon
Now we can calculate \( E \):
\[ E = \frac{(6.63 \times 10^{-34})(3 \times 10^8)}{663 \times 10^{-9}} \]
\[ E = \frac{1.989 \times 10^{-25}}{663 \times 10^{-9}} \]
\[ E \approx 2.998 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second
Now, we can find the number of photons emitted per second (N) using the formula:
\[ N = \frac{P}{E} \]
Substituting the values:
\[ N = \frac{60 \, \text{W}}{2.998 \times 10^{-19} \, \text{J}} \]

### Step 5: Calculate the number of photons
\[ N \approx \frac{60}{2.998 \times 10^{-19}} \]
\[ N \approx 2.00 \times 10^{20} \, \text{photons/s} \]

### Final Answer
The number of photons emitted per second by the 60 W source of monochromatic light of wavelength 663 nm is approximately:
\[ N \approx 2.00 \times 10^{20} \, \text{photons/s} \]

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