Question

You hold in your hands both a green \(543-n m, 5.00-m W\) laser and a red, \(633-\mathrm{nm}, 4.00\) -mW laser. Which one will produce more photons per second, and why?

Short answer

Answer: _____

Step-by-step solution

Before calculating the number of photons for each laser, we need to convert the given wavelengths (in nm) and powers (in mW) to their respective SI units: meters (m) and watts (W). We'll do this by using the following conversion factors: - 1 nm = 10^(-9) m - 1 mW = 10^(-3) W #Step 2: Calculate the energy of one photon for each laser#

Using the energy of one photon formula, we will calculate the energy of a single photon for both the green and red lasers: Energy of one green photon = (h * c) / λ (green) Energy of one red photon = (h * c) / λ (red) #Step 3: Calculate the number of photons per second for each laser#

Now, we will use the power of each laser and the energy of a single photon to compute the number of photons produced per second for both the green and red lasers: Number of green photons per second = (Power of green laser)/(Energy of one green photon) Number of red photons per second = (Power of red laser)/(Energy of one red photon) #Step 4: Compare the number of photons produced per second for both lasers#

Once we have calculated the number of photons per second for each laser, we will compare these numbers and determine which laser produces more photons. If the number of green photons per second > number of red photons per second, the green laser produces more photons. If the number of green photons per second < number of red photons per second, the red laser produces more photons.

Key concepts

Laser Physics

Lasers are fascinating devices that emit light through a process called stimulated emission. The word "laser" stands for Light Amplification by Stimulated Emission of Radiation. Lasers produce light that is highly monochromatic, meaning it has a single wavelength. This makes the light coherent and is often very intense.

Here's how a laser works internally:

• Gain Medium: The core material inside a laser where the light amplification takes place by exciting electrons to higher energy levels.
• Energy Source: Also known as a "pump," this provides the energy needed to excite the electrons in the gain medium.
• Optical Resonator: Consists typically of two mirrors facing each other, allowing the light to bounce back and forth, gaining energy with each pass.

Lasers have numerous applications, from medical treatments and cutting materials to communication and even entertainment. The precise control over the wavelength makes lasers an essential tool in many high-tech fields.

Photon Energy Calculation

To calculate the energy of a photon, we use the formula derived from Planck's equation: \[ E = \frac{h \times c}{\lambda} \]where:

• E is the energy of the photon in joules (J).
• h is Planck's constant, approximately \( 6.626 \times 10^{-34} \text{ J s} \).
• c is the speed of light in a vacuum, approximately \( 3.00 \times 10^8 \text{ m/s} \).
• \(\lambda\) is the wavelength of the light in meters (m).

This equation highlights an important relationship: the longer the wavelength, the lower the energy of the photon, and vice versa. For example, green light with a wavelength of 543 nm has higher energy photons compared to red light with a wavelength of 633 nm. This is because shorter wavelengths correspond to more energetic photons.

Wavelength Conversion

In the context of laser physics and photon calculations, converting measurements to appropriate units is crucial. Wavelengths are commonly given in nanometers (nm) in optics, so understanding unit conversions is necessary.

Here’s how to convert wavelength measurements:

• Nanometers to Meters: To convert from nanometers to meters, remember that \( 1 \text{ nm} = 10^{-9} \text{ m} \). So, a wavelength like 543 nm is converted to meters by multiplying by \( 10^{-9} \), giving \( 543 \times 10^{-9} \text{ m} \).

Similarly, for power, often given in milliwatts (mW), you convert to watts (W) since \( 1 \text{ mW} = 10^{-3} \text{ W} \). Therefore, a laser power of 5 mW is \( 5 \times 10^{-3} \text{ W} \).

Understanding these conversions is essential for performing accurate calculations in physics and engineering. Precision in units ensures correctness in determining photon numbers and comparing outputs of different lasers.