## 1.31

Kelly Cai 4D
Posts: 55
Joined: Sat Jul 20, 2019 12:17 am

### 1.31

In a recent suspense film, two secret agents must penetrate a criminal's stronghold monitored by a lithium photomultiplier cell that is continually bathed in light from a laser. If the beam of light is broken, an alarm sounds. The agents want to use a hand- held laser to illuminate the cell while they pass in front of it. They have two lasers, a high-intensity red ruby laser (694 nm) and a low-intensity violet GaN laser (405 nm), but they disagree on which one would be better. Determine (a) which laser they should use and (b) the kinetic energy of the electrons emitted. The work function of lithium is 2.93 eV.

Hannah Lee 2F
Posts: 117
Joined: Thu Jul 11, 2019 12:15 am

### Re: 1.31

The lithium photomultiplier basically means that upon absorption of a photon of light to the surface of the lithium cell, electrons are emitted. This implies that we are dealing with the photoelectric effect, and the laser the agents choose has to discharge enough energy/emit a high-enough frequency of light to eject electrons from the lithium surface. If the beam is "broken", then the laser has less energy than the criminal's laser (so no electrons are being discharged from the lithium cell) which triggers the alarm.

(a) You have to compare the energy of the two lasers to the work function using E = hv, and we can substitute v = c / λ so that it becomes E = h(c / λ). The work function is the minimum amount of energy it takes to eject an electron from the metal surface. After converting lithium's work function (eV) to joules and calculating the energies of low-intensity violet and high-intensity red lasers, we discover that the violet GaN laser is the better option. This is because the violet laser produces energy greater than the work function, so it has a high-enough frequency to eject e- from the lithium cell.
(b) To find the total KE of emitted e-, you rearrange the equation Ephoton = work function + KE and use: KE = Ephoton - work function. This produces (4.90 x 10-19 J) - (4.69 x 10-19 J) = 2.10 x 10-20 J.