Light of wavelength 575 nm is directed at a metallic surface with a work function of 1.60 eV.
(a) What is the maximum kinetic energy of an electron emitted from this surface, in J?
(b) What is the maximum speed of this electron? (m = 9.11 × 10-31 kg)
(c) What is the de Broglie wavelength of this electron?
In order to answer these questions, we need to apply the principles of the photoelectric effect and the de Broglie wavelength formula. Let's break it down step by step:
(a) To find the maximum kinetic energy of an electron emitted from the metallic surface, we can use the equation for the photoelectric effect:
E = hf - Φ
where E is the kinetic energy of the electron, h is Planck's constant (h = 6.626 × 10^-34 J·s), f is the frequency of the incident light (which we can calculate using the speed of light, c = 3.0 × 10^8 m/s, and the wavelength of light, λ), and Φ is the work function of the metal.
First, we need to convert the wavelength of light from nanometers to meters:
λ = 575 nm = 575 × 10^-9 m
Next, we can determine the frequency using the speed of light equation:
c = fλ
Rearranging the equation, we get:
f = c / λ
Substituting the values for speed of light and wavelength:
f = (3.0 × 10^8 m/s) / (575 × 10^-9 m)
Now we can calculate the maximum kinetic energy of the electron:
E = hf - Φ = (6.626 × 10^-34 J·s) × (f) - (1.60 eV)
To convert eV to joules, we can use the conversion factor:
1 eV = 1.602 × 10^-19 J
Substituting the values and calculating will give us the answer in joules.
(b) Once we have the kinetic energy of the electron, we can use the kinetic energy formula to find its maximum speed:
KE = (1/2)mv^2
Rearranging the equation to solve for velocity:
v = √[2(KE) / m]
Substituting the values for kinetic energy and mass, we can calculate the maximum speed of the electron.
(c) To find the de Broglie wavelength of an electron, we can use the formula:
λ = h / p
where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the electron.
The momentum of the electron can be calculated as:
p = mv
Substituting the values for mass and maximum speed, we can determine the de Broglie wavelength.