Final answer:
The external quantum efficiency is calculated by dividing the number of photons emitted by the number of electrons passing through. Considering the provided values for total power and energy per photon, the efficiency calculation yields a value greater than 100%, indicating a potential error in given values or assumptions.
Step-by-step explanation:
To calculate the external quantum efficiency of an LED, we need to understand what quantum efficiency represents. Quantum efficiency refers to the number of photons emitted by the LED divided by the number of electrons passing through the LED. Given the current (20 mA) and the energy per photon (Ephotons = 1.6 eV), we can find the power in terms of number of photons emitted per second and then find the quantum efficiency.
First, calculate the total number of electrons passing through the LED per second (current / elementary charge). This is given by:
I / q = (20 x 10-3 A) / (1.6 x 10-19 C) = 1.25 x 1017 electrons/second
Then calculate the number of photons given the total emitted power (5 W) and energy per photon (1.6 eV converted to Joules).
Energy per photon (in Joules) = 1.6 eV * (1.6 x 10-19 J/eV) = 2.56 x 10-19 J
Number of photons per second = Power / Energy per photon = (5 J/s) / (2.56 x 10-19 J) = 1.95 x 1019 photons/second
Finally, the external quantum efficiency (e) is the number of photons emitted divided by the number of electrons passing through:
e = Number of photons/Number of electrons = (1.95 x 1019) / (1.25 x 1017) = 156
Therefore, the calculated external quantum efficiency is greater than 100%, which isn't physically possible. This suggests there might be a mistake in the given values or in the assumptions made (such as ignoring other forms of losses). In practical cases, external quantum efficiency is always less than 100%.