Homework Question 1.33 [ENDORSED]

[Delilah Naranjo dis 3j]

The velocity of an electron that is emitted from a metallic surface by a photon is 3.6 x 10^3 km s^-1. What is the wavelength of the ejected electron?
No electrons are emitted from the surface of the metal until the frequency of the radiation reaches 2.50 x 10^16 Hz. How many much energy is required to remove the electron from the metal surface?

[Yiling Liu 1N]

For your first question, regarding the wavelength of the ejected electron:

We can utilize the equation λ = h / p, where h is Plank's constant and p is momentum, or the mass of electron x velocity of electron.

λ = (6.626 * 10^(-34))
-------------------------
(9.11 * 10^(-31)) (3.6*10^6))

In the numerator is Plank's constant. The value of the mass of an electron is also given in the textbook, which is 9.11 * 10^(-31) kg. It's important to use kg and not g in this case, since kg is the SI unit. It's also important to remember to convert the velocity, which is given in km/s, into m/s.

λ = 2.02 x 10^(-10) m

[Yiling Liu 1N]

For your second question, regarding how much energy is required to remove the electron from the metal surface:

We recall the equation E = hv.

v is given in the problem as 2.50*10^16 Hz, and h is Plank's constant, or 6.626*10^(-34) J.s

plugging in the values, E = 1.66*10^(-17) J