The laser emits approximately \(7.08 \times 10^{15}\) photons per second.
To determine the number of photons emitted per second, you can use the formula:
\[ \text{Number of photons} = \frac{\text{Power output}}{\text{Energy per photon}} \]
The energy of a photon (\(E\)) can be calculated using the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \ \text{J}\cdot\text{s}\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 \ \text{m/s}\)),
- \(\lambda\) is the wavelength of light.
Let's calculate the energy per photon and then use it to find the number of photons emitted per second.
Given:
- Wavelength (\(\lambda\)) = 533 nm = \(533 \times 10^{-9} \ \text{m}\),
- Power output = 25 mW = \(25 \times 10^{-3} \ \text{W}\).
**Step 1:** Calculate the energy per photon (\(E\)) using the wavelength:
\[ E = \frac{hc}{\lambda} \]
**Step 2:** Use the calculated \(E\) to find the number of photons:
\[ \text{Number of photons} = \frac{\text{Power output}}{\text{Energy per photon}} \]
Now, let's perform the calculations.
**Step 1: Calculate the energy per photon (\(E\))**
\[ E = \frac{hc}{\lambda} \]
\[ E = \frac{(6.626 \times 10^{-34} \ \text{J}\cdot\text{s})(3.00 \times 10^8 \ \text{m/s})}{533 \times 10^{-9} \ \text{m}} \]
\[ E \approx 3.54 \times 10^{-19} \ \text{J} \]
**Step 2: Calculate the number of photons**
\[ \text{Number of photons} = \frac{\text{Power output}}{\text{Energy per photon}} \]
\[ \text{Number of photons} = \frac{25 \times 10^{-3} \ \text{W}}{3.54 \times 10^{-19} \ \text{J}} \]
\[ \text{Number of photons} \approx 7.08 \times 10^{15} \ \text{photons/second} \]
Therefore, the laser emits approximately \(7.08 \times 10^{15}\) photons per second.