Complete the table of particles involved in radioactive decay.

$$\begin{matrix} \text{Particle Name} & \text{Symbol} & \text{Mass Number} & \text{Atomic Number or Charge}\\ \text{alpha particle} & \ {_2 ^4He} & \text{ } & \text{ }\\ \text{ } & \ {^0 _{-1} e} & \text{ } & \text{-1}\\ \text{gamma ray} & \ {^0 _0 Y} & \text{ } & \text{ }\\ \text{positron} & \text{ } & \text{0} & \text{ }\\ \text{ } & \ {^1 _0 n} & \text{1} & \text{ }\\ \text{proton} & \ {^1 _1 p} & \text{ } & \text{ }\\ \end{matrix}$$

An electron that has an instantaneous velocity of

$$\vec { v } = \left( - 5.0 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s } \right) \hat { \mathrm { i } } + \left( 3.0 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s } \right) \hat { \mathrm { j } }$$

is moving through the uniform magnetic field

$$\vec { B } = ( 0.030 \mathrm { T } ) \hat { \mathrm { i } } - ( 0.15 T ) \hat { j }$$

. (a) Find the force on the electron due to the magnetic field. (b) Repeat your calculation for a proton having the same velocity.

Protons having a kinetic energy of

$$5.00 \mathrm{MeV}(1 \mathrm{eV}=1.60 \times \left.10^{-19} \mathrm{J}\right)$$

are moving in the positive x direction and enter a magnetic field $\overrightarrow{\mathbf{B}}=0.0500 \hat{\mathbf{k}} T$ directed out of the plane of the page and extending from x = 0 to x = 1.00 m. (a) Ignoring relativistic effects, find the angle $\alpha$ between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. (b) Calculate the y component of the protons' momenta as they leave the magnetic field.

On a lab exam, you have to find the concentrations of the monoprotic (one proton per molecule) acids HA and HB. You are given 43.5 mL of HA solution in one flask. A second flask contains 37.2 mL of HA, and you add enough HB solution to it to reach a final volume of 50.0 mL. You titrate the first HA solution with 87.3 mL of 0.0906 M NaOH and the mixture of HA and HB in the second flask with 96.4 mL of the NaOH solution. Calculate the molarity of the HA and HB solutions.

A helium atom has a rest mass of $m_{\text {Helium }}=4.002603 \mathrm{u}$. Its constituent particles (2 protons, 2 neutrons, 2 electrons), when well-separated, have the following masses: $m_{\text {proton }}=1.007276 \mathrm{u}, m_{\text {neutron }}=1.008665 \mathrm{u}$ and $m_{\text {electron }}=0.000549 \mathrm{u}$ How much work is required to completely disassemble a helium atom? (Recall that 1 u of mass has a rest energy of 931.5 MeV.)

Indicate whether each of the following statements about magnesium isotopes is true or false.

a. $^{24}_{12}\text{Mg}$ has one more proton than $^{25}_{12}\text{Mg}$

b. $^{24}_{12}\text{Mg}$ and $^{25}_{12}\text{Mg}$ contain the same number of subatomic particles.

c. $^{24}_{12}\text{Mg}$ has one less neutron than $^{25}_{12}\text{Mg}$.

d. $^{24}_{12}\text{Mg}$ and $^{25}_{12}\text{Mg}$ have different mass numbers.

Complete the table of particles involved in radioactive decay.

An alien from a planet in the galaxy $\mathrm{M} 31$ (Andromeda) has a ray gun that shoots protons at a speed of $2.0 \times 10^{5} \mathrm{m} / \mathrm{s}$. Design a magnetic shield that will deflect the protons away from your body. Using rough estimates, show that your magnetic shield will, in fact, protect you. Indicate the orientation of your protective device’s magnetic field relative to the direction of the proton beam and the direction in which the ions are deflected.

At the Stanford Linear Accelerator, electrons and positrons collide together at very high energies to create other elementary particles. Suppose an electron and a positron, each with rest energies of 0.511 MeV, collide to create a proton (rest energy 938 MeV), an electrically neutral kaon (498 MeV), and a negatively charged sigma baryon (1197 MeV).

What is the minimum kinetic energy the electron and positron must have to make this reaction occur? Assume they each have the same energy.

A hydrogen atom consists of an electron, of mass m, orbiting a proton, of mass M, where m is much smaller than M. The reduced mass, $\mu,$ of the hydrogen atom is defined by $\mu=\frac{m M}{m+M}.$

(a) Show that $\mu \approx m.$

(b) To get a more accurate approximation for $\mu,$express $\mu$ as m times a series in m/M.

(c) The approximation $\mu \approx m$ is obtained by disregarding all but the constant terms in the series. The first-order correction is obtained by including the linear term but no higher terms. If $m \approx M / 1836,$ by what percentage does including the linear term change the estimate $\mu \approx m ?$

Calculate the force on an electron in each of the following situations: $3.0 \times 10^{−6}$ m from a proton. Use the following: $q_{e}=-1.6 \times 10^{-19} \mathrm{C}$; $m_{e}=9.1 \times 10^{-31} \mathrm{kg}$; $q_{p}=1.6 \times 10^{-19} \mathrm{C}$; $c=3.0 \times 10^{8} \mathrm{m} / \mathrm{s}$; $k_{C}=9.0 \times 10^{9} \mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}$.

A reaction that has been considered as a source of energy is the absorption of a proton by a boron-11 nucleus to produce three alpha particles: $_ { 1 } ^ { 1 } \mathrm { H } + _ { 5 } ^ { 11 } \mathrm { B } \rightarrow 3 \left( _ { 2 } ^ { 4 } \mathrm { He } \right)$ This reaction is an attractive possibility because boron is easily obtained from Earth’s crust. A disadvantage is that the protons and boron nuclei must have large kinetic energies for the reaction to take place. This requirement contrasts to the initiation of uranium fission by slow neutrons. How much energy is released in each reaction?

One of the important ways in which the Higgs boson was detected at the Large Hadron Collider was by observing a type of decay in which the Higgs—which decays too quickly to be observed directly—is immediately transformed into two photons emitted back to back. Two photons, with momenta $3.31 \times 10^{-17} \mathrm{kg} \mathrm{m} / \mathrm{s}$, were detected. What is the mass of the Higgs boson? Give your answer as a multiple of the proton mass. Hint: The relationship between energy and momentum applies to photons if you treat a photon as a massless particle.

A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at $1.50 \mathrm{~km} / \mathrm{s}$ in the $+x$-direction experiences a force of $2.25 \times$ $10^{-16} \mathrm{~N}$ in the $+y$-direction, and an electron moving at $4.75 \mathrm{~km} / \mathrm{s}$ in the $-z$-direction experiences a force of $8.50 \times 10^{-16} \mathrm{~N}$ in the $+y$-direction. (b) What are the magnitude and direction of the magnetic force on an electron moving in the $-y$-direction at $3.20 \mathrm{~km} / \mathrm{s}$ ?