A laser with a power output of 2 mW at a wavelength of 400 nm is projected onto a calcium metal surface. What power is carried away by the electrons? The binding energy of the metal is 2.31 eV.
To determine the power carried away by the electrons, we need to calculate the number of photons that are absorbed by the calcium metal surface and then use the binding energy of the metal to find the power.
Step 1: Calculate the energy of each photon
The energy of each photon can be calculated using the formula:
Energy = (Planck's constant * speed of light) / wavelength
Since the power output is given in milliwatts, and 1 milliwatt is equal to 1/1000 watts, we need to convert it to watts:
Power = 2 mW = 2/1000 W = 0.002 W
Wavelength = 400 nm = 400 * 10^(-9) m
Plugging the values into the formula, we can calculate the energy of each photon:
Energy = (6.626 x 10^(-34) J·s * 3 x 10^8 m/s) / (400 x 10^(-9) m)
Step 2: Calculate the number of photons
To calculate the number of photons, we'll use the formula:
Number of photons = Power / Energy
Plugging in the values we have:
Number of photons = 0.002 W / Energy
Step 3: Calculate the power carried away by the electrons
The power carried away by the electrons can be determined by multiplying the number of photons by the binding energy of the metal:
Power carried away = Number of photons * Binding energy
Plugging in the values we have:
Power carried away = Number of photons * 2.31 eV
However, we need to convert the binding energy from electron volts (eV) to joules (J) because the energy of each photon was calculated in joules:
Binding energy = 2.31 eV = 2.31 * 1.6 x 10^(-19) J
Now we can substitute the values:
Power carried away = Number of photons * Binding energy
Finally, replace the calculation for the number of photons to get the final answer.