Introduction to Units Practice Problems

The earth's circumference is approximately 40.1 Mm (megameters). What is this circumference in kilometers?

Express the following number using powers of 10:

0.5438

What is the fully expanded form, including any necessary zeros, of the number represented by 7.3 × 10²?

Express the Earth-to-Sun distance, approximately 93 million miles with two significant figures, in 'miles' using powers of 10 notation.

The average distance between the Earth and the Moon is approximately 238,855 miles. Calculate this distance in meters and express it using a metric prefix(km).

Express the following measurement in complete decimal form, without using any unit prefixes: 9.8 µm

The position of a free falling object at any instant is given by the equation: y = ½ gt², where y and t have units of meter and seconds, respectively. Determine the unit of constant 'g'.

If you sailed due east from a point on Earth's equator until you reached a new longitude 10 minutes of arc away (keeping your latitude constant), what distance in nautical miles would you have covered? Note that there are 60 minutes per degree of longitude. Consider Earth's radius as 3,440 nautical miles.

A company producing digital thermometers states that its thermometers have an accuracy of no more than ±0.100°C. Calculate the accuracy of these thermometers as a percentage of the temperature range they measure (if they measure from -20.0°C to 100.0°C).

If the mass of the cruise ship is 2.13 ×10⁸ kg, calculate the approximate number of protons or neutrons in it.

The order of magnitude is the rough estimation of the approximate size or value given in the power of ten. Estimate the order of magnitude of 85.25 × 10⁴.

When manufacturing precision-engineered components for a spacecraft, the length of a critical component needs to be determined with extreme accuracy. If this component should have a length of 30 cm to within ±0.1 mm, what percentage of uncertainty in the length is permissible, and how many significant figures should be used in the measurement of the length?

Consider a particle with a radius of 2.2×10⁻⁵ m. If the particles are arranged end-to-end, determine roughly how many particles would fit along a 2.4 cm line.

If θ is specified as 60.0° ± 0.3°, compute the percentage of uncertainty in both i) cos(θ) and ii) θ.

Consider a scenario in a chemistry laboratory where you are measuring the volume of a liquid using a standard graduated cylinder. Normally, there is an uncertainty of approximately 2 mL because reading the meniscus precisely can be challenging. Determine the percent uncertainty for a volume measurement of: 75 mL.

Determine how many scooters can be stored in a 3200 m² warehouse. Assume the scooters are organized in a grid pattern, with 0.82 meters-wide- walkways. Each scooter is boxed in a square box and occupies 1.8 m² of floor space.

If two moles of carbon atoms were uniformly spread on the surface of a 121 m long and 52 m wide rectangular field, determine the number of atoms per square meter.

Consider you're on a beach where you see a floating object at one end which is 1.8 m above sea level as shown in the figure. When you are 3.8 km away from the object the top of the object is just barely visible. Assuming that your line of sight to the top of the object aligns perfectly with the Earth's surface at that point, determine the radius R of the Earth.

A rectangular field 282 m long and 118m wide, is being mowed by a smaller commercial grade mower which has a speed of 4.0 km/h and a cutting width of 2.4m. Determine the time it would take to mow this field.

A group of bikers are on a 250 km long route, traversing various landscapes. They covered the first 70.0 km in one day. Estimate how long it will take them to cover the remaining distance.

A 1.5 L bottle is filled with nearly spherical candies. Estimate how many candies are there in the bottle if the radius of a candy is 0.5 cm.

Calculate the surface area of the planet Venus. The diameter of Venus is 12100 km.

A 3.0 m long, 1.5 m wide, and 0.75 m deep pond is completely filled with water. Only 0.02% of this water contains minerals. If the average density of these minerals is 6.0 × 10^-4 kg/L, estimate how many minerals (in kg) are present in the pond.

Express the following measurement using the prefixes commonly used in the International System of Units (SI): 0.457 × 10⁴ meters.

A bullet has a mass of 25.2 g. The bullet is already moving and is to be given an acceleration of 2.5 m/s² in the same direction as its current velocity. Use relativity to determine the force required when the velocity is i) 320 m/s ii) 0.800c iii) 0.950c

A neutron moves at 0.75c. Its momentum is p. If the speed is divided by 1.5, express the new momentum in terms of p.

A neutron of mass m is at rest. A force F gives the neutron an acceleration a, when it is at rest. When the neutron moves at a speed v, the force required to produce the same acceleration a, is 2.5F. Determine the value of v in terms of the speed of light, c.

Alpha particles have a charge +2e and a rest mass of 6.645 × 10^-27 kg. An accelerator changes the energy of an alpha particle so that its overall energy is 2.5E₀, where E₀ is the rest energy. i) Calculate the particles' kinetic energy ii) Find the momentum (magnitude only) of the particle iii) determine the speed of the alpha particle.

A particle accelerator uses a 2.0 MV potential difference to accelerate a hydrogen ion (proton), giving it a kinetic energy of 5.60 × 10⁵ eV. i) Express the proton's velocity magnitude as a fraction of the speed of light, c. ii) Use Newtonian laws of motion to determine the proton's speed.

A lithium atom has a rest mass of 1.17 × 10⁻²⁶ kg. For an atom whose momentum magnitude is 1.5 × 10^-18 kg•m/s, determine i) the sum of kinetic and rest energy of the atom, ii) the atom's kinetic energy, iii) The ratio of the atom's rest energy to kinetic energy.

Relativistic effects will be experienced when an object exceeds 0.1c, where c is the speed of light.  The mass of a neutron is 1.6749 × 10^-27 kg. Determine the ratio K_nr/K_r (r - relativistic and nr - non-relativistic) when the neutron moves at i) 0.2c and ii) 0.8c

An unstable particle released during a nuclear disintegration has an average lifetime of 2.2 microseconds. A particle is released 5.00 km away from a detector. The speed of the particle in the atmosphere approaches the speed of light at v = 0.995c. i) Determine the average lifetime of the particle as measured by an observer at rest and ii) the distance covered by the particle during the time measured by the observer at rest. iii) Use the answers in part i) and ii) to state what you think about the possibility of the particle hitting the detector. 

A high-energy particle accelerator produces unstable particles moving along the horizontal axis at a speed of 0.810 c in the laboratory frame. At rest, these particles decay with an average lifetime of 0.80 μs. Calculate the lifetime of the particles measured with a detector fixed in the laboratory.

Highly energetic particles originating from cosmic rays approach the surface of Earth with a speed close to the speed of light. The k-meson (or Kaon) reaches the Earth's atmosphere with a speed of 0.88c. The mean lifetime of a K-meson at rest is 1.23 × 10⁻⁸ s. Calculate the average distance,  as measured from Earth's frame,  the K-meson particles travel before decaying.

Two synchronized stopwatches are placed in two spaceships, A and B. Spaceship A is traveling with a velocity of 0.6c relative to Spaceship B. When spaceship A passes spaceship B, the two stopwatches start to count time simultaneously. i) Determine the time (t _A) displayed on the stopwatch of spaceship A when spaceship A has moved 0.75 × 10 ⁸ m in front of spaceship B. ii) What is the distance separating the two spaceships at the instant when the stopwatch in spaceship A displays the time t _A. iii) What time (t _B) does the stopwatch of spaceship B display when the stopwatch of spaceship A displays the time t _A?

A control tower operator detects a red light pulse emitted from an unidentified flying object (UFO) in the Earth's atmosphere at a speed of v. The control tower operator measures the pulse duration to be 1.3 s. A passenger on the UFO observes that the light pulse lasts for 1.1 s. i) Who measures the proper time interval for the duration of the pulse? ii) Express the speed v of the UFO in the Earth's frame as a function of the speed of light c.

Imagine a scenario where a spacecraft maintains a steady velocity, moving horizontally to the right relative to Earth. Within this spacecraft, an observer positioned at its center observes two laser beams - one green, on the left side, and the other blue, on the right side - striking the endpoints of the spacecraft simultaneously as shown in the figure below. Concurrently, an observer stationed on Earth observes the same two events. From the perspective of the Earth-based observer, which of the two events occurred first?

Consider a hydrogen atom confined within a rigid cubical box with sides of length l, where the volume of the box is equal to the volume of a sphere with radius r = 4.13 × 10^-11 m. Determine the energy separation between the ground and the second excited state within the context of the particle in a box model, and compare this with the energy separation predicted by the Bohr model.

Consider a quantum particle (m = 9.11 × 10 ^-31 kg )that lies inside a 3D cubical box. The side of the box is 5.00 × 10^-11 m in length and the probability of finding the particle outside the box is zero. When the particle jumps from an excited state  (n_x = 2, n_y = 1, n_z = 2) to a ground state( n_x = 1, n_y = 1, n_z = 1) a photon of wavelength, λ is emitted. Calculate the wavelength, λ of the emitted photon.

The principal quantum number is 3 when the electron is in an nth M-shell. What should be the lowest value of its orbital angular momentum? Write your answer in multiples of ħ and in SI units where ħ = h/2ℼ.

An electron transitions from the M-shell to the N-shell. Determine the highest value of its orbital angular momentum after the transition. Write your final answer in terms of ħ.

Consider a model system for the simplest element hydrogen. Find the largest orbital angular momentum in the z-direction if the electron moves in an L-circular orbit.

When n = 3 it corresponds to the second excited state of the Bohr hydrogen atom. If the electron is in the M shell what does this tell you about the smallest spin angular momentum this electron could have in any arbitrary direction?

The azimuthal quantum number describes the general shape of an electron orbital. If an electron's orbital angular momentum is exactly 3.63 × 10^-34 kg•m²/s what should its angular momentum quantum number (ℓ) be where ℓ, is the quantum number associated with the angular momentum of an electron?

The energy of an electron is mainly determined by the values of the principal and orbital quantum numbers.  For the given principal quantum numbers n = 3, n = 10, and n = 150 in a hydrogen atom, calculate the maximum orbital angular momentum l.  Express your answer in terms of ħ. What pattern do you see? Also, compare the values of nħ with the Bohr model.

The presence of a magnetic field splits the spectral lines into groups of closely spaced lines. Now consider an f-state hydrogen atom placed in an external magnetic field of 0.500 T where the field is applied in the +z axis. Due to the interaction of the atom's orbital magnetic moment with the applied magnetic field, the energy levels associated with orbital angular momentum (m_l) split. Determine the energy difference between adjacent m _l levels. Give the final answer in electron volts.

Atoms are composed of charged particles, so the presence of a uniform magnetic field 'B'  causes a change in their motion and energy levels. When a hydrogen atom in the 3d state is placed in a uniform magnetic field 'B' it splits into multiple energy levels as the electron's orbital magnetic moment interacts with the external magnetic field. Determine the magnitude of the applied magnetic field 'B' required to split the levels when the adjacent levels have an energy difference of 5.35 × 10^-5 eV.

In the context of the Bohr model, consider an electron in a hydrogen atom transitions from a 3p excited state to a 1s ground state. After the transition, a uniform magnetic field is applied, causing the energy levels to split. Ignore the spin effect. Determine the m_l values for the initial and final states for the transition.

Consider a hydrogen atom in the 3d state placed in an external magnetic field of 0.400 T. The applied magnetic field is uniform and is in the z-axis. In an external field, degeneracy is disrupted, and spectral lines are separated. Find out how many levels the state 3d splits due to this interaction. 

Consider a negatively charged particle (electron) that is assumed to be perfectly spherical in shape. The negatively charged elementary particle that orbits the atom's nuclei has a radius of 2.14 x10^-14 m and the magnitude of its spin angular momentum is (6/7)^1/2 ħ. Find its angular speed (ω) and the speed ν of a point at the equator of the negatively charged particle. What can you say about the model's validity based on your results?

A split in an energy level of a system occurs when a perturbation changes the system. This may occur because of external fields. Consider the case where the perturbation splits the degenerate ground level into two distinct levels separated by 4.8 x 10^-6 eV. What should be the wavelength and frequency of the emitted photon when the atom has jumped between these states? Also, find the region of the electromagnetic spectrum in which they fall.

Consider a quantum simulator for interacting spin systems with complete control of individual interactions. In the initially set parameters, a magnetic field in which the 1s state atom is placed is 1.25 T and is in the positive z-direction. All the model parameters can be dynamically tuned at will. Considering the applied parameters, determine the energy difference between the spin-up and the spin-down state and find which level (m_s =1/2 or m_s = -1/2)  is at the lowest energy.

In atomic physics, the total angular momentum is obtained by combining its orbital and spin angular momentum. Assume the case of a hydrogen atom with principal quantum number n = 2 and orbital quantum number l = 1. What should be the energy difference between the two possible values j = 1/2 and j = 3/2?

Find the energy required to move the electron from level n with energy E_n to level n = ∞ with energy E_∞ = 0 (Ionization energy) when the effective charge attracting a 4s electron in potassium is 2.20 e.

In an experiment, the energies of some unknown element 5s, 5p, and 5d states are measured to be E_s = -3.43 eV, E_p =-2.21 eV, and E_d = -0.54 eV. Determine the value of the effective (screened) atomic number Z_eff for each state. What pattern do you observe in Z_eff based on your findings?

The sodium-ion battery  (SIB) is a  rechargeable battery that uses sodium ions (Na⁺) as charge carriers. The sodium atom (Na) loses its outer electron to become a sodium ion (Na⁺). Write the electronic configuration of Na⁺ ion in its fundamental state.

If the effective nuclear charge of Al²⁺ is 3. What should be the energy of the most loosely bound level in the M shell of Al²⁺

Find the effective (screened ) atomic number Z_eff for the 3s fundamental state of sodium. The measured value of energy for the 3s state is approximately -5 eV.

Find how much energy the highest l state has for magnesium Mg⁺ (M shell) and strontium  Sr⁺ (O shell).

A high-energy beam in a particle accelerator knocks a K-shell electron of an atom, creating a vacancy (hole) in the K-shell. This vacancy can be filled by the electron in the L, M, or N shell. Each shell has a distinct energy: the electron's energy in the K-shell is -68,500 eV, L-shell is -11,000 eV and M-shell is -2100 eV. Determine the wavelength of the characteristic x-rays i) K_α and ii) K_β

The spacing between two nuclei of CO molecule is 0.1135 nm. Consider the mass of the carbon atom as 1.993 × 10^-26 kg and that of the oxygen atom as 2.656 × 10^-26 kg. A transition from l = 3 to l = 2 results in the emission of a photon. Determine its wavelength.

The energy of an atom is decreased by 8.90 eV and a photon is released in the process. Determine the photon's wavelength and the electromagnetic spectrum in which it lies.

An O₂ molecule undergoes a transition from l = 2 to l = 3 rotational levels by absorbing a photon. Calculate the wavelength of the absorbed photon if the moment of inertia of the O₂ molecule is 1.94 × 10^-46  kg•m²

The spacing between two nitrogen atoms in an N₂ molecule is 0.130 nm. Consider an axis which is a perpendicular bisector of the line joining the centre of gravity of both atoms each having a mass of 2.32 × 10^-26 kg. Determine the moment of inertia about this axis.

The rotational energy of an O₂ molecule is 0.358 meV for l=1 rotation level with a moment of inertia of 1.94 × 10^-46  kg•m² with respect to an axis passing through the center of mass and perpendicular to the line joining the two oxygen atoms. Calculate the rotating molecule's rotation speed for l = 1 level if the rotational energy of the molecule is related to angular speed by the relation E = (1/2)•I•w².

Calculate the O₂ molecule's linear speed for l = 2 rotation level if the rotational energy of the O₂ molecule is related to angular speed by the relation E =  (1/2)•I•w². Consider the rotational energy of the O₂ molecule as 1.075 meV with a moment of inertia of 1.94 × 10^-46  kg•m² about an axis passing through the center of mass and perpendicular to the line joining the two oxygen atoms.

The expression (3/2)kT, where T is the temperature in Kelvin, describes an ideal gas's average kinetic energy per molecule. Find the temperature at which the energy difference between the l = 0 and l = 1 levels of the O₂ molecule is equal to the average kinetic energy. The moment of inertia of the O₂ molecule is 1.94 × 10^-46  kg•m². Also, comment if there will be enough excited electrons at room temperature.

A gallium arsenide light detector can detect light of a maximum wavelength of 0.874 μm. Determine this detector's bandgap energy in eV between valence and conduction bands.

State true or false 'Pure germanium is largely opaque to visible light.' Consider a germanium light detector with a maximum capacity to detect a light of wavelength 3.82 μm.

Considering electrons as completely free particles within a conductor, determine the number of states per unit energy range (g(E)). The energy E of states at the surface is 6.5 eV and V = 1.5 cm³. State g(E) in terms of states per electron volt.

For a metal at 310 K and at constant volume, determine the contribution of electron to the molar heat capacity. Take the Fermi energy of metal as 6.32 eV and the molar gas constant is 8.314 J/mol.K.

The Fermi temperature for metal is approximately the temperature at which molecules in a classical ideal gas would have the same kinetic energy as the fastest-moving electron in the metal. Consider Fermi energy E_f = k•T_f where T_f is the Fermi temperature, and calculate the occupancy probability for a state with energy E = 3E_f.

What is the probability that the bottommost state of the conduction band of pure silicon is occupied for temperatures of (i) 275 K (ii) 325 K (iii) 375 K? The bandgap for pure silicon is 1.12 eV and Fermi energy is exactly at halfway in the bandgap.

Determine the spectrum and also the magnitude of wavelength that can be detected by a light detector which works on the principle that conductivity increases with an increase in the electron-hole pairs. The band gap energy for the semiconductor material used is 1.42 eV.

Calculate the magnitude of the current flowing through a diode's p-n junction with a standard saturation current value as IS = 0.450 mA when the voltage is i) -50 mV and ii) 150 mV. The diode is placed at a temperature of 285 K

A current of 7.50 mA flows through a p-n junction diode when a forward voltage of 12.0 mV is connected across it. Determine the new value of current through the diode when the voltage is changed to 17.0 mV at 310 K

While conducting an NMR experiment, a physicist placed a sample of protons in a magnetic field. The protons are in a low-energy, or "spin-up," state. Each of these protons can absorb a photon and undergo spin flipping to the higher energy "spin-down" state if the photon's energy matches the energy difference between the two states.  For the NMR experiment to work, determine the magnitude of the magnetic field that will guarantee a spin flip between the energy levels if the photons have a frequency of 64 MHz.

The concentration of carbon-14 (), a radioactive isotope of carbon, is used to determine the age of organic materials. The atomic mass of carbon-14 is about 14.003241 u. Find i) the mass defect (Δm), ii) the total binding energy (E_B), and ii) the binding energy per nucleon of carbon-14.

A physics student claims that carbon-14 decays according to the equation  i) Evaluate the validity of his claim. If you agree with the student calculate the energy released during the decay. ii) Repeat part i) if the student claims that a cobalt-60 decays according to the equation  .

 Determine the daughter isotope that is produced by the following reaction: i) negative β decay of Phosphorus ( ), ii) α decay of radium , and iii)   positive β decay of carbon ()

Show that the β⁺ decay of , according to the equation , is energetically possible and calculate the energy produced. ²²Na has an atomic mass of 21.994438 u and ²²Ne has an atomic mass of 21.9913851u and a positron has a mass of 0.0005486 u.

Complete the decay equation for the given unstable nuclide by indicating the type of released subatomic particles.

i)

ii)

iii)

Radioactive iodine (I-131) is used to treat certain types of thyroid gland cancer. A patient receives a 250 mCi dose of iodine. Calculate the activity of iodine 30 days after getting radioactive therapy. The activity of a sample of iodine decays over time, with a half-life of 8.07 days.

In brachytherapy, a sealed source of radium 226 is used to deliver a radiation dose to a certain tumor. Radium-226 has a half-life of 1600 years and decays by producing radon 222 and an alpha particle. i) Calculate the decay constant of radium-226. A patient needs a dose of 20 mCi to treat his cancer. ii) Calculate the mass of radium designed to be swallowed by the patient. iii) Calculate the rate of emission of alpha particles for a 1 μg sample of radium-226.

The decay of rubidium 87 (Rb) is employed to estimate the age of a very old mineral sample containing 3.25 g of Rb. i) Calculate the number of radioactive disintegrations per second within this sample if Rb has a half-life of 4.92×10¹⁰ years. ii) Express the activity of this sample in Ci.

A Geiger-Müller tube counts 650 disintegrations per second at a time t = 0 originating from an Iodine 131 sample. After 24 hours it counts 597 disintegrations per second. Calculate the half-life T_1/2 of Iodine.

Medical imaging has improved diagnosis and treatment by substantially reducing the necessity for exploratory surgeries and other potentially dangerous practices. Medical imaging uses ionizing radiation such as x-rays to create images of the human body. Unfortunately, the cumulative radiation dose increases the risk of cancer. For instance, during a whole-body computed tomography (CT), a 65 kg adult receives an effective dose of 16 mSv. Alternatively, during abdominal x-ray imaging, 4.0 kg of tissue receives an effective dose of 0.7 mSv. Find the ratio of the amount of energy transferred to the body during CT to the amount of energy transferred to the 4.0 kg of tissue during abdominal x-ray imaging.

Accidentally, a health worker receives ionizing radiation with a wavelength of 1.5 nm. The mass of the affected forearm tissue is 2.00 kg. Assume that 4.15 × 10⁸ photons are absorbed by the forearm. Calculate i)  the amount of energy deposited in the forearm and ii) the effective dose of the radiation received by the forearm in rem.

A tritium atom and a deuterium atom combine to form helium-4 according to the equation: . Calculate the energy produced during this nuclear reaction.

A fluorescent lamp emits red light of wavelength 640 nm. For a single photon in the light determine the photon's momentum, its energy in J as well as eV and also the frequency.

A laser device was used for the light show during a musical performance. The laser device emitted pulses each of 25.0 ms with an average power of 0.700 W. For each pulse calculate the energy in J and eV if the wavelength of light emitted is 562 nm.

Consider a photon in the light emitted by a laser device that has a momentum of 7.23 × 10^-28 kg•m/s. Determine in which part of the electromagnetic spectrum this photon's wavelength lies.

The infrared radiation of frequency 2.52×10¹⁵ Hz causes electrons to eject from a metal surface. What will be the maximum kinetic energy of the electrons ejected in electron volts if the photoelectric threshold wavelength of the metal surface is 500 nm?

Ultraviolet light with a wavelength range of 100 nm - 400 nm is incident on a lithium surface. Determine the minimum value of the work function for the lithium surface to eject electrons.

In a photoelectric experiment, a light of wavelength 230 nm falls on sodium. Calculate the stopping potential in volts if sodium has a photoelectric work function of 2.7 eV.

A light of wavelength 270 nm is incident on the magnesium surface which ejects electrons from the surface. Determine the kinetic energy of the most energetic electrons ejected if the photoelectric function of magnesium is 3.68 eV.

Roentgen tubes are evacuated electron tubes used to produce x-rays. Determine the shortest wavelength of the x-rays produced if the accelerating potential inside the tube is 17.0 kV

Calculate the wavelength of the Compton scattered x-rays at a scattering angle of 45 degrees. X-rays undergoing Compton scattering have an initial wavelength of 0.0543 nm.

A photon of light bounces back into its initial direction of motion after colliding with an electron. The angle between the initial and final direction of the photon is 180°. The wavelength of the photon increases by 5% following the scattering. Determine the wavelength of the incident photon.  

Electromagnetic waves of wavelength 0.065 nm are incident on a material. The waves experience Compton scattering. The wavelength of the scattered waves is greater than the wavelength of incident waves by 2.5%. Calculate the scattering angle.

A neutron and alpha particles are emitted during a nuclear disintegration. They both have the same speed, 0.650c measured in a laboratory frame. Determine the kinetic energy of i) neutron ii) alpha particle. 

In a collider, a muon (-e) and its anti-particle(+e), initially at rest, collide head-on and turn into two photons. The muon has an electric charge +e, and a mass equals 207 times the mass of an electron. Determine the energy, frequency, and wavelength of each photon Also, find the region of the electromagnetic spectrum in which the photons lie.

A muon decays into an electron and a  pair of neutrinos. The mass of muon is m = 207 m_e. Determine the maximum muon wavelength for this event (ignoring neutrinos). Also, describe the electron's motion right after the event.

Muons are massive particles and a  muon (-e) and antimuon (+e) could transform into an electron(-e) and a positron(+e). Initially, if massive particles were at rest determine the energy, frequency, and wavelength of the electron and its anti-particle. Assume an electron's mass (m) is approximately 200 times less than the mass (M) of the muon.

Determine the energy available when there is a collision between a stationary positive electron and a moving electron with a total energy of 28.6 GeV.

An alternating voltage at a frequency of 8.00 MHz is applied to a cyclotron in which tritons are emerging from the two hollow semicircular electrodes of the cyclotron after moving in a circular path of a radius of 35.0 cm. Determine the magnitude of the magnetic field generated.

Calculate the frequency of the potential across the hollow semicircular electrodes of a cyclotron if a magnetic field of 1.65 T is used to accelerate protons.

Alpha particles with an energy of 18.0 GeV are bombarded on stationary helium gas atoms. Determine the total energy of the beam particle.

In an experiment performed in the laboratory, protons are travelling at a very high speed. If the total energy of a proton is 980 GeV, find the speed of the proton.

Consider the collision between two protons (m_pc²=938.25 MeV ) giving a deuteron (m_dc²= 1875.6MeV) and a π⁺ meson (m_π+c²=139.6MeV) according to the equation p+p →d + π⁺. What is the threshold energy of this reaction?

Consider a colliding beam setup where two beams of electrons are accelerated and directed against each other at the same energy. Calculate the energy of each of the colliding beams if the available energy produced in such a setup is 124 MeV.

Two highly energetic protons beam, having the same energy collide, with each other. Calculate the minimum kinetic energy that each proton beam must have in order to obtain the following reaction:p+p→p+p+π⁺ + π^-

A short-lived neutral hadronic particle ρ⁰ decays into two pions subatomic particles. Write the decay equation.

According to the equation K⁺ → μ⁺ +ν_μ, a stationary kaon decays into a muon and a muon neutrino. Calculate the energy released during the decay.

A stationary η⁰ meson decays into two energetically similar γ rays. Calculate the energy of each of the γ rays.

The Σ⁰ particle is a baryon with strangeness –1. A stationary Σ⁰ particle decays according to the following equation Σ⁰→Λ⁰ + γ. Calculate the γ ray's momentum. Assume that the kinetic energy of Λ⁰ is negligible.

A physicist is studying the decay of the neutral particle Λ⁰.  Λ⁰ is at rest.  Λ⁰ decays according to  Λ⁰ → n +π⁰. What would be the expected combined kinetic energy of the n and π0 particles after the decay?

A stationary η⁰ particle decays via the following electromagnetic interaction η⁰→  π^- +  π^- +  π⁰. Calculate the total kinetic energy of the three emitted pions (π).

In two climate-controlled lab rooms, scientists simulate extreme temperatures. One replicates the coldest temperature (T_l) ever recorded, -120 °F, and the other the highest (T_h), 132 °F. Calculate these temperatures in Celsius and Kelvin degrees.

A researcher has invented a novel temperature measurement system known as the "M scale." In this scale, the boiling point of argon is defined as 0°M, while the melting point of aluminum is assigned a value of 1000°M. If an object is measured to have a temperature of 320°M on this scale, what would be its temperature in kelvins? The boiling point of argon is -185.7^oC and the melting point of aluminum is 660.3^oC.

Considering the given situation in the figure below, what can you conclude about the particle's motion (bending upwards, bending downwards, or traveling in a straight line)?

Find the units of the product of L and C, where L represents the inductance of an inductor and C represents the capacitance of a capacitor.