Question

Calculate the average power output (in watts) of a photodetector that collects 8.0 x 107 photons in 3.8 ms from monochromatic light of wavelength (a) 470 nm, the wavelength produced by some commercially available light-emitting diodes (LED), and (b) 780 nm, a wavelength produced by lasers that are commonly used in compact disc (CD) players. Hint: The total energy emitted by a source or collected by a detector in a given interval is its power multiplied by the time interval of interest (1 J = 1 W s).

Answer 1

`8.90392* 10^(-9)\ W`

`5.36518* 10^(-9)\ W`

Step-by-step explanation:

h = Planck's constant =
`6.626* 10^(-34)\ m^2kg/s`

c = Speed of light =
`3* 10^8\ m/s`

t = Time taken = 3.8 ms

`\lambda` = Wavelength

n = Number of protons =
`8* 10^7`

Power is given by

`P=(E)/(t)\\\Rightarrow P=(nh(c)/(\lambda))/(t)\\\Rightarrow P=(8* 10^7* 6.626* 10^(-34)* (3* 10^8)/(470* 10^(-9)))/(3.8* 10^(-3))\\\Rightarrow P=8.90392* 10^(-9)\ W`

The power is
`8.90392* 10^(-9)\ W`

`P=(nh(c)/(\lambda))/(t)\\\Rightarrow P=(8* 10^7* 6.626* 10^(-34)* (3* 10^8)/(780* 10^(-9)))/(3.8* 10^(-3))\\\Rightarrow P=5.36518* 10^(-9)\ W`

The power is
`5.36518* 10^(-9)\ W`