Physics 132-04 Test 3

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Questions (5 for 8 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.

1. During the radioactivity laboratory you made several runs with the radiation counter with no radioactive sources nearby. Why?

   
   
   
   
   
   
   
   

2. Radiocarbon dating relies on the observation that the fraction of $\rm ^{14}C$ in living organisms has been at least roughly constant for many thousands of years. How can this be if the $\rm ^{14}C$ is constantly decaying away?

   
   
   
   
   
   
   
   
   

3. In building the theory behind the two-slit interference pattern we derived an expression for the intensity of pure, 2-slit interference (no diffraction effects). The result is shown in the top figure below. The measured result for the intensity looks more like the bottom figure. Why are the two so different?

4. Recall the laboratory on conservation of angular momentum where you analyzed a rotational collision where a cylindrical weight of mass $m_w$ and radius $r_w$ was dropped on a rotating disk and ended up revolving about the origin at a distance $r_r$. The distance $r_r$ is from the center of the rotator to the center of the dropped weight. Generate an expression for the moment of inertia of the dropped weight in terms of the quantities listed here.

5. Induction furnaces are commonly used in industry to take advantage of electromagnetic induction to heat metals. How would such a device work and what things would you need to build one?

Problems (3). Clearly show all reasoning for full credit. Use a separate sheet to show your work.

1.

18 pts.

The figure below shows a plane, electromagnetic, sinusoidal wave propagating in the $x$ direction. The wavelength is $\lambda = 40~m$ and the electric field $\vec E$ vibrates in the $xy$ plane with an amplitude $E_m = 22.0~V/m$. What is the frequency $f$ of the wave, the magnitude $B_m$ of the magnetic field $\vec B$, and the full expression for $\vec B$ with the proper unit vector in terms of $B_m$, $\lambda$, and $f$? Justify your choice of trigonometric function used to describe the wave.

DO NOT WRITE BELOW THIS LINE.

2.	18 pts.	The radionuclide $\rm ^{64}Cu$ has a half-life of $t_{1/2} = 12.7~ h$. How many nuclei from an initially pure, 10-g sample of $\rm ^{64}Cu$ will decay during the 3.0-hour period beginning 10.0 hours later?
3.	24 pts.	Laser light with a wavelength $\lambda = 632.8~nm = 6.328\times 10^{-7}~m$ is directed through one slits or two slits and falls on a screen a distance $L = 2.60~m$ away. The figure below shows the pattern on the screen with a centimeter ruler below it. Did the light pass through one slit or two slits? Explain your reasoning. It the light passed through one slit find its width. If the light passed through two slits find the distance between their centers.

Physics 132-4 Constants

Avogadro's number ($N_A$)	$6.022\times 10^{23}$	Speed of light ($c$)	$3\times 10^8~m/s$
$k_B$	$1.38\times 10^{-23}~J/K$	proton/neutron mass	$1.67\times 10^{-27}~kg$
$1 ~ u$	$1.67\times 10^{-27}~kg$	$g$	$9.8~m/s^2$
Gravitation constant	$6.67 \times 10^{-11}~N-m^2/kg^2$	Earth's radius	$6.37\times 10^6~m$
Coulomb constant ($k_e$)	$8.99\times 10^{9} {N-m^2 \over C^2}$	Electron mass	$9.11\times 10^{-31}~kg$
Elementary charge ($e$)	$1.60\times 10^{-19}~C$	Proton/Neutron mass	$1.67\times 10^{-27}~kg$
Permittivity constant ($\epsilon_0$)	$8.85\times 10^{-12} {kg^2\over N-m^2}$	$\rm 1.0~eV$	$1.6\times 10^{-19}~J$
$\rm 1 ~MeV$	$10^6 ~ eV$	atomic mass unit ($u$)	$1.66\times 10^{-27}~kg$

Physics 132-4 Equations

$$\vec F = m \vec a = \frac{d\vec p}{dt} \quad a_c = \frac{v^2... ... s \quad KE = {1 \over 2} mv^2 \quad KE_0 + PE_0 = KE_1 + PE_1$$

$$\vec p = m \vec v \quad \vec p_0 = \vec p_1 \quad x = \frac{a}{2} t^2 + v_0 t + x_0 \quad v = at + v_0$$

$$E = \frac{1}{2} mv_r^2 + \frac{L^2}{2mr^2} + PE(r) \quad L =... ..._i^2 \quad I = I_{cm} + MD^2 \quad I_0 \omega_0 = I_1 \omega_1$$

$$\vec F_C = k_e \frac{q_1 q_2}{r^2}\hat r \quad \vec E \equiv... ... {q_n \over r_n} \quad V = k_e \int {dq \over r} \quad PE = qV$$

$${d N \over d t} = - \lambda t \quad N = N_0 e^{-\lambda t} ... ...\omega t) \quad k\lambda = 2 \pi \quad \omega T = 2 \pi \quad$$

$$E = E_m \sin (kx - \omega t) \quad B = B_m \sin (kx - \omega... ... \quad E = cB \quad \vert\vec S\vert = I =\frac{E^2}{2\mu_0 c}$$

$$I = 4 I_0 \cos^2 \left ( {\pi d \over \lambda} \sin \theta \... ... \theta \right )}{\frac{\pi a}{\lambda} \sin \theta}\right ]^2$$

$$\delta = d \sin \theta = m \lambda\ (m=0,\pm 1,\pm 2,...)\qu... ...) \quad \phi = k\delta \quad \sin \theta_R = {\lambda \over d}$$

$${1 \over \lambda} = R_H \left ( {1 \over n_f^2} - {1 \over n_i^2} \right ) \quad E_n = - \frac{13.6~eV}{n^2} \quad$$

$$-\frac{\hbar^2}{2 m}\left ( \frac{d^2}{d r^2} \right ) \Psi(... ...) + U(r) \Psi(r) = E \Psi(r) \quad E = hf = \frac{hc}{\lambda}$$

$${d \over dx}(x^n) = nx^{n-1} \quad {d \over dx}(f(u)) = {df\... ...x^n dx = {x^{n+1} \over n+1} \quad \int \frac{1}{x} dx = \ln x$$

$$\frac{d e^x}{dx} = e^x \quad \frac{d}{dx}(\ln x) = \frac{1}{... ... (\cos ax) = -a\sin ax \quad {d \over dx} (\sin ax) = a\cos ax$$

$$\langle x\rangle = \frac{1}{N}\sum_i x_{i} \quad \sigma = \s... ...} \quad A = 4\pi r^2 \quad V = Ah \quad V = {4\over 3} \pi r^3$$

The Periodic Chart.