A positron and an electron can annihilate each other on colliding, producing energy as photons:

$${_{-1}^{0} e}+{_{+1}^{0} e} \longrightarrow 2_{0}^{0} \gamma$$

Assuming that both $\gamma$ rays have the same energy, calculate the wavelength of the electromagnetic radiation produced.

Owls have good night vision because their eyes can detect a light intensity as low as $5.0 \times 10^{-13} \mathrm{~W} / \mathrm{m}^2$. Calculate the number of photons per second that an owl's eye can detect if its pupil has a diameter of $9.0 \mathrm{~mm}$ and the light has a wavelength of $500 \mathrm{~nm}$. $(1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}$.

Write the sentence in symbolic form, using the given symbols.

Let p represent "It is hot." Let q represent "It is raining." Let r represent "The sky is cloudy."

It is not hot.

For the compound statement in symbolic form: a. Write a complete sentence in words to show what the symbols represent. b. Tell whether the compound statement is true or false. ~g → ~ j

Find the derivatives. Assume that a, b, and c are constants. $f ( t ) = a e ^ { b t }$

Show that for a system of atoms and photons in equilibrium at a temperature T the ratio of the transition rates of stimulated to spontaneous emission is given by $\left[\frac{1}{e^{\frac{h v}{h \pi}}-1}\right]$.

A monochromatic lightbulb $(\lambda=650 \mathrm{~nm})$ emits $45 \mathrm{~W}$ of power. If you stand $15 \mathrm{~m}$ from this bulb, how many photons enter each of your eyes per second? Assume your pupil is $5.0 \mathrm{~mm}$ in diameter and that the bulb radiates uniformly in all directions.

The amount of heat to melt ice is $0.333 \mathrm{kj} / \mathrm{g}.$ Find the number of photons of wavelength $=6.42 \times 10^{-6} \mathrm{m}$ that must be absorbed to melt $5.55 \times 10^{-2} \mathrm{mol}$ of ice.

Let p and q represent the following simple statements: p: Rom eo loves Juliet. q: Juliet loves Romeo. Write each symbolic statement in words.

$$\sim p \wedge q$$

Consider a microscopic spring-mass system whose spring stiffness is $50 \mathrm{N} / \mathrm{m},$ and the mass is $4 \times 10^{-26} \mathrm{kg}.$ In a collection of these microscopic oscillators, the temperature is high enough that the ground state and the first three excited states are occupied. What are possible energies of photons emitted by these oscillators?

In a photoelectric experiment using a clean sodium surface, the maximum energy of the emitted photons was measured for a number of different incident frequencies, with the following results.

$$\begin{matrix} \ {Frequency \ (10^{14} Hz)} & \ {Energy (eV)}\\ \text{11.8} & \text{2.60}\\ \text{10.6} & \text{2.11}\\ \text{9.9} & \text{1.81}\\ \text{9.1} & \text{1.47}\\ \text{8.2} & \text{1.10}\\ \text{6.9} & \text{0.57}\\ \end{matrix}$$

Plot the graph of these results and find: (a) Planck's constant; (b) the cutoff frequency of sodium; the work function.

The Zeeman effect occurs in sodium just as in hydrogen—sodium's lone 3s valence electron behaves much as hydrogen's 1s. Suppose sodium atoms are immersed in a 0.1 T magnetic field.(a) Into how many levels is the $3p_{1/2}$ level split?(b) Determine the energy spacing between these states.(c) Into how many lines is the $3p_{1/2}$ to $3s_{1/2}$ spectral line split by the field?(d) Describe quantitatively the spacing of these lines.(e) The sodium doublet (589.0 nm and 589.6 nm) is two spectral lines, $\rightarrow 3 s^{1 / 2}$ and $3 p^{1 / 2} \rightarrow 3 s^{1 / 2}$ which are split according to the two different possible spin-orbit energies in the 3p state. Determine the splitting of the sodium doublet (the energy difference between the two photons). How does it compare with the line splitting of part (d), and why?

Let p and q represent the following simple statements: p: Romeo loves Juliet. q: Juliet loves Romeo. Write each symbolic statement in words. $\sim(q \wedge p)$

A helium-neon laser produces a beam of diameter 1.75 mm, delivering $2.00 \times 10^{18}$ photons/s. Each photon has a wavelength of 633 nm. If the beam shines perpendicularly onto a perfectly reflecting surface, what force does it exert on the surface?