Question

Electromagnetic radiation with a frequency of 8.6 ´ 1014 hz incident on an unknown metal surface causes ejection of photoelectrons with kinetic energies of 1.3 ´ 10–19 j. what is the unknown metal?

Answer 1

This looks like the photo electric effect and Einstein's equation to "solve" it.
Energy of the photon is E = h frequency, h is planck's constant. Hopefully that will come out in Joules. Then, if you subtract from the photon energy the KE of the electron what's left is the work function of the metal. from that, and a table of them, you can work out which metal it is. (For some reason, my mind thinks "sodium".)

Answer 2

Answer: The unknown metal is Sodium.

Explanation: Photoelectric effect happens when a metal surface is hit by a monochromatic eletromagnetic wave causing the surface to emit electrons, which is the case for question.

To determine the metal, we have to find Φ or work function (W), which is the energy necessary to detach a photoelectron from the surface:

W = hf - KE

where:

h is Planck's constant and equals 6.63.
`10^(-34)` J/s;

f is the frequency of the wave;

KE is kinetic energy the electron has the instant it detaches from the surface;

W = hf - KE

W = 6.63.
`10^(-34)`. 8.6.
`10^(14)` - 1.3.
`10^(-19)`

W = 57.018.
`10^(-20)` - 1.3.
`10^(-19)`

W = 4.4.
`10^(-19)` eV

The element which uses this amount of energy to detach an electron is Sodium (Na).