Textbook Focus 1B #15

[Emily Hou 1H]

The velocity of an electron that is emitted from a metallic surface by a photon is 3.6 x 10^3 km/s
(a) What is the wavelength of the ejected electron?

For this question, why can't we solve it by finding the kinetic energy (Ke= 1/2(9.11 x 10^-31)(3.6*10^6 m/s)^2 ) then using that to solve for the wavelength?
The correct answer in the textbook is solved by the de Broglie equation

[Caleb_Mei_1J]

Hey Emily!

Since we don't quite know the frequency of the photon that was used to excite the electrons on the metal surface, the work function cannot be calculated. Thus, de Broglie's wavelength equation is used because all of the variables besides wavelength are known.

I hope this helps!

[AudreyQian1J]

Hello,

I believe that it is better to not assume that the velocity of the ejected electron can be used to find the excess energy (Ek), because the problem did not mention if the electron had just enough or more energy than the work function. It is also safer to use Ek=1/2mv^2 when we need to use Ephoton - work function = Ek.
De Broglie's equation is used to find wavelength of particles with rest mass. Since the electron has mass, using the De Broglie's equation is simpler.

I hope this helps.