PHYS 415/417 MIDTERM
Mar 4, 2015
Number and answer each question. Place a box around your final answer. Show your work for
full credit. Specify units on your answers please.
hc = 2 x 10-25 J-m = 1240 eV-nm, c=3x108 m/s e= 1.6 x 10-19 C
Stephan-Boltzmann constant = 5.7 e-8 W/m2-K4
Wein Displacement constant = 2.90e-3 m-K
Planck’s constant = 6.663e-34 J-s = 4.14 e-15 eV-s
1T = 1.e4G
1- Describe and state the purpose of the Millikan Oil Drop experiment. Write the force on the oil
droplets and briefly describe each term. How did Millikan know that charge was quantized?
Millikan used charged oil droplets to measure the fundamental unit of charge by bringing them to
rest in a electrostatic chamber. The applied electrostatic forces can be used to determine the oil
droplet’s charge. These charge were determined have charges with multiples of “e”.
F = mg +/-qE - bv
gravitational force, electrostatic force, and drag force.
1 1
2- Two spin =1/2 electrons are in the n:s p -state . What total values of angular momentum
J=L+S can occur? Express you answer in 2S +1 LJ spectroscopic notation. What is the lowest
energy state?
S = 1/2+1/2 = 0, 1 L= 0 + 1 = 1
J = L+S = (1+0) , (1+1) = (1) (2,1,0)
1
P1 3P2,1,0
Lowest energy state: Highest L,S and lowest J => 3P0
3- Quantities x1 = 5 x 2 = 6 x 3 = 10 x 4 = 3 are measured. Determine the mean x , standard
deviation, σrms , and standard deviation of the mean σ x of the measured quantities.
x_avg = 24/4 = 6
with N=4
sig = sqrt( 1+0+16+9 )/sqrt(4-1) ~ 5/sqrt(3) = 2.9
sig_xavg =sig/sqrt(N) = 2.9/2 = 1.5
4 - In a photoelectric experiment the stopping potential is found to be 3.11 V when light of
170nm is shone on a certain metal. What is the work function of the metal?
KEmax=eV=hf-W
hf = E = 1240/170 = 7.3 eV
3.11 eV = 7.30eV – W
W = 4.2 eV
5- The Bohr magneton for an orbital electron with µ B = e! / 2me . The nuclear magneton for a
proton in a nucleus is µ B = e! / 2m p . (a) What is the accepted value for the gyromagnetic ratio g
of the electron and proton based on the Spin Resonance experiment ? (b) Find the resonant
spin-flipping frequency f for protons in organic tissue placed in a 2T magnetic field.
g=2
and hf =g u_B x B
f = (2/h) (e hbar/2m) B = (e B/ pi m ) = 6.1e7Hz
1
6- Find the mean and σ r.m.s. of the following numbers: 4, 2, 1, 3, 5 . What is the error on the
mean? ( 2 decimal places please).
x_mean = 15/5 = 3.00
rms = sqrt[(4-3)^2+(2-3)^2+(1-3)^2+(3-3)^2+(5-3)^2]/ sqrt[ 5] = sqrt(10/5)=1.41
err_mean = rms/sqrt(N)=0.63
7- The excitation energy in a gallium arsenide LED is 1.92eV. What wavelength of light that is
emitted?
Lambda = 1240 eV-nm/1.92eV = 645nm
+v
8- A velocity dependent force is given by F(v) = F0 e . From Newton’s Law of motion,
determine an expression for v(t), where v(0) = 0.
m dv/dt = Fo exp(v)
exp(-v)dv = (Fo/m)dt
-exp(-v) = (Fo/m)t + C
exp(-v) = -(Fo/m)t – C
1 = -C v(0) = 0
exp(-v) = [1-(Fo/m)t ]
v = -ln [1-(Fo/m)t ]
9- Based on the solar sprectrum-1 given on page 2, what is the average temperature of the sun’s
photosphere?
Lambda_max~ 500 nm
o
T =b/Lambda_max = b/ 500nm = 2.9e-3 m-K / 500nm = 5800 K
10- Based on the absorption spectra of the water molecule Spectra-2 what is the dominant
absorption energy of the molecule in eV?
Lambda_abs ~ 500 nm
E =1240eV-nm / 500nm = 2.48 eV
2
2
Spectra -1 Spectra of the sunlight: W/m vs wavelength in nm
AM0 ASTM E490
2.5
2.0
1.5
W*m-2*nm-1
1.0
0.5
0.0
0
500
1000
1500
2000
2500
3000
3500
4000
Spectra -2 Absortion spectra of light in water.
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