Bohr model
Interference & diffraction
Fourier series
Quantumy shenanigans
Special mystery category
100
What is Bohr's quantization condition?
L = nℏ
Allowed values of the orbital angular momentum are integer multiplies of the constant ℏ.
100
When is destructive interference observed in single-slit diffraction?
asinθ=mλ,for m=±1,±2,±3,...
100
Is this function even or odd?
Even: f(-x) = f(x)
100
What is the formula for the maximum kinetic energy of a photoelectrically emitted photon?
Kmax = hf - ϕ
100
Binomial approximation formula???
(1+ϵ)n ≈ 1 + nϵ
200
What are the allowed energy levels of a hydrogen-like ion?
En = -Z2ER/n2, where Z is the nuclear charge and ER is the Rydberg energy (13.6 eV).
200
When is constructive interference observed in a 2-slit experiment? When is destructive interference observed?
Constructive interference: dsinθ=mλ
Destructive interference: dsinθ=(m+1/2)λ
200
Is this function even or odd?
Odd: f(-x)=-f(x)
200
What is the formula for the change in wavelength due to Compton scattering?
Δλ=(h/mc)(1-cosθ)
200
Let z=4-6i.
What is Re(z)? What is Im(z)?
Re(z) = 4
Im(z) = -6
300
What is the radius of the n=1 orbit of an O7+ ion?
(Taylor 15.16)
0.00661 nm
300
What is the angle of the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm?
("University Physics" volume 3, 3.17)
0.997 degrees.
300
What is the fundamental frequency? What is the frequency of the greatest harmonic with substantial amplitude? (Units of the x-axis are seconds)
fundamental freq: 0.5 Hz
3rd harmonic: 1.5 Hz
300
A metal's work function is ϕ=3.4 eV. What is the maximum wavelength of photoelectrically emitted light?
365 nm
300
I have (-3+4i) boxes of cookies. Each box has (3+i) cookies in it. How many cookies do I have?
-13+9i cookies.
400
An electron in a He+ ion drops from the 4th energy level to the 2nd. What wavelength of light is emitted?
122 nm (ultraviolet)
400
A double slit with d = 0.0750 mm is located 1.00 m away from a screen, and 500 nm light falls on the slit. What is the distance of the 3rd intensity maximum from the center of the screen?
2.00 cm
400
What is the fundamental frequency? What is the frequency of the greatest harmonic with substantial amplitude? (Units of the x-axis are seconds)
Fundamental frequency: 0.25 Hz
3rd harmonic: 0.75 Hz
400
What is the moon's de Broglie wavelength?
About 8.8 * 10-60 m.
400
Come up with your own problem relating to interference/diffraction, the Bohr model, Fourier series, or another subject from this midterm's material. Then solve the problem! :)
:)
500
A muon has mass mμ=207me. If captured by a proton, what is the radius and energy of the 1st Bohr orbit? What wavelength of light is emitted if the muon drops from the 2nd energy level to the 1st?
(Taylor 5.13)
Radius = 0.000256 nm
Energy = 2800 eV
Wavelength = 0.59 nm
500
A Michelson interferometer uses light of wavelength 632.8 nm. One of its mirrors is moved by a distance D, and 8 fringes move past the field of view. What is the value of D?
("University Physics", volume 3, 3.51)
D = 2531.2 nm
500
Find a general formula for the Fourier coefficients of the square wave.
Bm = (1/mπ)(1-2cos(mπ)+cos(2mπ))
500
A particle's wavefunction squared is given by |ψ(x)|2=(2/π)sqrt(1-x2). What is the uncertainty in its position?
Δx = 1/2
500
A particle's wavefunction squared is given by |ψ(x)|2=(2/π)sqrt(1-x2). The uncertainty in its position is Δx=1/2. Apply the binomial approximation to the wavefunction, then calculate the uncertainty (only integrate over the regions where |ψ(x)|2 is positive in the approximation). How does this uncertainty compare to Δx=1/2?
Δx≈0.693. The uncertainty is greater than the version without the binomial approximation.