A metal surface has a work function of 2.50 eV. What is the longest wavelength of light that will eject electrons from the surface of this metal?

Question

BlackTom AI · Accepted Answer

We are told the metal has a work function φ = 2.50 eV. For photoemission to occur, the photon energy E = hc/λ must be at least φ. The longest wavelength that can cause emission is the threshold wavelength where E = φ, so λ_max = hc/φ.

Using the common value hc ≈ 1240 eV·nm, we get λ_max ≈ 1240 / 2.50 ≈ 496 nm. This means wavelengths around 496 nm are just energetic enough to overcome the work function.

Now evaluate each option:
- 797 nm: photon energy E = 1240/797 ≈ 1.56 eV, which is less than φ. Insufficient energy to overcome the work function, so no emission occurs.
- 397 nm: photon energy E = 1240/397 ≈ 3.13 eV, which is greater than φ. Emission will occur, and electrons will have kinetic energy of roughly E − φ ≈ 0.63 eV.
- 197 nm: photon energy E = 1240/197 ≈ 6.30 eV, well above φ. Emission will occur with substantial kinetic energy, about 6.30 − 2.50 ≈ 3.80 eV.
- 497 nm: photon energy E = 1240/497 ≈ 2.50 eV, essentially equal to φ. This is the threshold case, so emission is possible with near-zero kinetic energy.

Therefore, among the choices, 497 nm corresponds to the longest wavelength that can just eject electrons, while the shorter-wavelength options would also eject electrons but at higher photon energies.

PHYSICS 1201 SU2025 (10585) Quiz 8- Requires Respondus LockDown Browser

A metal surface has a work function of 2.50 eV. What is the longest wavelength of light that will eject electrons from the surface of this metal?

View Explanation

Log in for full answers

Similar Questions

A light source hits the surface of platinum metal and no electrons are emitted. What change should be made to the light source to eject electrons? 12A

Infrared light shined on a metal initially emits no electrons. What is the quantum prediction if the intensity of the light is increased?

Energy absorbed by an electron is used in

The photoelectric emission confirms

Infrared light shined on a metal initially emits no electrons. What is the classical prediction if the intensity of the light is increased?

It is observed that light of 430 nm just begins to emit photoelectrons. What is the quantum prediction if the wavelength of the incident light is changed to 440 nm?

Which of the following statements is incorrect?

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler