Red light with a wavelength of 660 nm from a 3.0 mW diode laser shines on a solar cell. (b) How much current (in amperes) flows in the circuit of the solar cell if all the photons are absorbed by the cell and each photon produces one electron?

Verified step by step guidance

1. insert step 1> Calculate the energy of a single photon using the formula: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (6.626 \times 10^{-34} \text{ J s}), \( c \) is the speed of light (3.00 \times 10^8 \text{ m/s}), and \( \lambda \) is the wavelength (660 \text{ nm} = 660 \times 10^{-9} \text{ m}).
2. insert step 2> Convert the power of the laser from milliwatts to watts: 3.0 \text{ mW} = 3.0 \times 10^{-3} \text{ W}.
3. insert step 3> Calculate the number of photons emitted per second by dividing the power of the laser by the energy of a single photon: \( \text{Number of photons per second} = \frac{\text{Power}}{E} \).
4. insert step 4> Since each photon produces one electron, the number of electrons produced per second is equal to the number of photons per second.
5. insert step 5> Calculate the current using the formula: \( I = \frac{\text{Number of electrons per second} \times e}{1} \), where \( e \) is the elementary charge (1.602 \times 10^{-19} \text{ C}).

Key Concepts

Photon Energy

The energy of a photon is determined by its wavelength, calculated using the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. For red light at 660 nm, this energy is crucial for understanding how many photons are needed to generate a specific amount of current in the solar cell.

Current and Charge

Current (I) is defined as the flow of electric charge per unit time, measured in amperes (A). In this context, if each absorbed photon generates one electron, the total current can be calculated by determining the number of electrons produced per second, which directly relates to the number of photons absorbed by the solar cell.

Power and Energy Conversion

The power output of the laser (3.0 mW) indicates the rate at which energy is delivered. To find the current, we need to relate this power to the energy produced by the photons. The relationship between power, energy, and time allows us to calculate how many photons are emitted per second and, consequently, how many electrons (and thus current) are generated in the solar cell.