Question

A laser source emits light of wavelength 300nm and has a power of 3.3mW. The average number of photons emitted per second is:(Speed of light-3x10⁸m/s,Plank's constant 6.6 x 10^-34J/s)

• A. 2x10¹⁵
• B. 1x10¹⁵
• C. 5x10¹⁵
• D. 3x10¹⁵
• E. 4x10¹⁵

Answer 1

The Correct Option is C

Given:

• Wavelength of light, \( \lambda = 300 \, \text{nm} = 300 \times 10^{-9} \, \text{m} \)
• Power of laser, \( P = 3.3 \, \text{mW} = 3.3 \times 10^{-3} \, \text{W} \)
• Speed of light, \( c = 3 \times 10^8 \, \text{m/s} \)
• Planck's constant, \( h = 6.6 \times 10^{-34} \, \text{J} \cdot \text{s} \)

Step 1: Calculate Energy per Photon

The energy of a single photon is given by:

\[ E = \frac{h c}{\lambda} \]

Substitute the given values:

\[ E = \frac{(6.6 \times 10^{-34}) (3 \times 10^8)}{300 \times 10^{-9}} \]

\[ E = \frac{19.8 \times 10^{-26}}{300 \times 10^{-9}} \]

\[ E = 6.6 \times 10^{-19} \, \text{J} \]

Step 2: Determine Number of Photons per Second

The number of photons emitted per second (\( n \)) is the total power divided by the energy of one photon:

\[ n = \frac{P}{E} \]

\[ n = \frac{3.3 \times 10^{-3}}{6.6 \times 10^{-19}} \]

\[ n = 0.5 \times 10^{16} = 5 \times 10^{15} \]

Conclusion:

The average number of photons emitted per second is \( 5 \times 10^{15} \).

Answer: \(\boxed{C}\)

Answer 2

Step 1: Recall the formula for the energy of a photon.

The energy of a single photon (\( E \)) is given by:

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

where:

• \( h = 6.6 \times 10^{-34} \, \text{J·s} \) is Planck's constant,
• \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light, and
• \( \lambda = 300 \, \text{nm} = 300 \times 10^{-9} \, \text{m} \) is the wavelength of the light.

 

Substitute the values to calculate the energy of one photon:

\[ E = \frac{(6.6 \times 10^{-34})(3 \times 10^8)}{300 \times 10^{-9}}. \]

Simplify:

\[ E = \frac{19.8 \times 10^{-26}}{300 \times 10^{-9}} = \frac{19.8 \times 10^{-26}}{3 \times 10^{-7}} = 6.6 \times 10^{-19} \, \text{J}. \] ---

Step 2: Calculate the total number of photons emitted per second.

The power of the laser (\( P \)) is the total energy emitted per second. The total number of photons emitted per second (\( N \)) can be calculated as:

\[ N = \frac{P}{E}, \]

where:

• \( P = 3.3 \, \text{mW} = 3.3 \times 10^{-3} \, \text{J/s}, \) and
• \( E = 6.6 \times 10^{-19} \, \text{J}. \)

 

Substitute the values:

\[ N = \frac{3.3 \times 10^{-3}}{6.6 \times 10^{-19}}. \]

Simplify:

\[ N = 0.5 \times 10^{16} = 5 \times 10^{15}. \] ---

Final Answer: The average number of photons emitted per second is \( \mathbf{5 \times 10^{15}} \), which corresponds to option \( \mathbf{(C)} \).