A laser pointer used in the classroom emits light at 5650 Å, at a power of 4.00 mW. (One watt is the SI unit of power, the measure of energy per unit of time. 1 W = 1 J/s). How many photons are emitted from the pointer in 115 seconds?

To determine the number of photons emitted from the laser pointer in a given time, we need to know the energy of each photon and the total energy emitted over that time period.

First, let's calculate the energy of one photon.

The energy \(E\) of a photon can be calculated using the equation:

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

where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the light.

Given that: - \(h\), Planck’s constant, is approximately \(6.626 \times 10^{-34}\) Joule-seconds (J·s) - \(c\), the speed of light, is approximately \(3.00 \times 10^8\) meters per second (m/s) - \(\lambda\), the wavelength of the laser light, is \(5650 \) Angstroms (\(\text{Å}\)). Note that 1 \(\text{Å}\) = \(10^{-10}\) meters.

First, we need to convert the wavelength from Ångstroms to meters:

\[ \lambda = 5650 \text{Å} \times 10^{-10} \text{m/Å} = 5.650 \times 10^{-7} \text{m} \]

Now, we can calculate the energy of one photon (\(E\)):

\[ E = \frac{(6.626 \times 10^{-34} \text{J·s}) \times (3.00 \times 10^8 \text{m/s})}{5.650 \times 10^{-7} \text{m}} \] \[ E = \frac{1.9878 \times 10^{-25} \text{J·m}}{5.650 \times 10^{-7} \text{m}} \] \[ E \approx 3.517 \times 10^{-19} \text{J} \]

Next, the total energy \(E_{total}\) emitted by the laser pointer over 115 seconds can be calculated by multiplying the power by the time:

\[ E_{total} = \text{power} \times \text{time} \] \[ E_{total} = 4.00 \times 10^{-3} \text{W} \times 115 \text{s} \] \[ E_{total} = 4.60 \text{J} \]

Given that 1 Watt (W) is equivalent to 1 Joule per second (J/s), and \(E_{total}\) is measured in Joules (since \(E_{total}\) = power (J/s) \(\times\) time (s)).

The number of photons \(N\) emitted is then the total energy divided by the energy per photon:

\[ N = \frac{E_{total}}{E} \] \[ N = \frac{4.60 \text{J}}{3.517 \times 10^{-19} \text{J/photon}} \] \[ N \approx 1.308 \times 10^{19} \text{ photons} \]

So, approximately \(1.308 \times 10^{19}\) photons are emitted from the laser pointer in 115 seconds.

Extra: The concept of a photon relates to quantum mechanics, where light can behave both as a wave and as a particle. This duality is known as wave-particle duality. When considering light as particles, we talk about these particles as photons, which are quanta of light. Each photon carries a discrete amount of energy that corresponds to the light's wavelength or frequency. The relationship between energy and wavelength is inverse; that means shorter wavelengths (higher frequency light) have more energy per photon, while longer wavelengths (lower frequency light) have less energy per photon.

In classroom settings, laser pointers are used because they can project a small, bright spot onto various surfaces. The coherence and low dispersion of laser light allow the beam to stay narrow over long distances, making laser pointers useful for pointing out details on, for example, a screen or a blackboard. However, it's important to understand laser safety, as even low-powered lasers can cause damage to the eyes if used improperly.