I apologize if my previous response came across as dismissive. I understand that you need help, and I'm here to assist you.
The photoelectric effect can be described by the equation:
E = hf - φ
Where:
E is the kinetic energy of the emitted electron
h is the Planck's constant (6.626 x 10^(-34) J·s)
f is the frequency of the incident light
φ (phi) is the work function of the surface (the minimum energy needed to remove an electron from the surface)
Now, let's apply this equation to the given information.
(a) To determine the work function (φ), we need to use the equation with the known values of E, h, and f. We need to find the frequency (f) from the given wavelength (λ) of the incident light:
c = λf
Where:
c is the speed of light (approximately 3.00 x 10^8 m/s)
λ is the wavelength of the light (400 nm = 400 x 10^(-9) m)
Rearranging the equation, we get:
f = c / λ
Substituting the values, we have:
f = (3.00 x 10^8 m/s) / (400 x 10^(-9) m)
Now, we can use this value of frequency (f) along with the given kinetic energy (E) to solve for the work function (φ):
E = hf - φ
Note that the kinetic energy is related to the speed (v) of the emitted electron by:
E = (1/2)mv^2
Where:
m is the mass of the electron (9.109 x 10^(-31) kg)
You can rearrange this equation to solve for v:
v = √(2E / m)
Substituting the given kinetic energy (E) and mass (m), you can calculate the speed (v) of the emitted electron.
(b) The threshold frequency (f_threshold) is the minimum frequency required to start the emission of electrons from the surface. In this case, we need to find the frequency (f_threshold) that gives us a kinetic energy (E) of zero.
Setting E = 0 in the equation E = hf - φ, we get:
0 = hf_threshold - φ
Now, you can solve for the threshold frequency (f_threshold) using the known value of the work function (φ).
(c) The de Broglie wavelength (λ_db) of a particle is related to its velocity (v) by the equation:
λ_db = h / mv
You can substitute the given maximum velocity (v) into this equation along with the mass of the electron (m) to find the de Broglie wavelength (λ_db) of the electron.
Remember to use the correct units for all quantities (e.g., joules, meters, seconds) and be mindful of conversion factors if necessary.
I hope this explanation helps. Let me know if you have any further questions.