Show transcribed image text A certain commercial mass spectrometer (see Sample Problem 28 - 3) is used to separate uranium ions of mass 3.92 times 10 - 25 kg and charge 3.20 times 10 - 19 C from related species. The ions are accelerated through a potential difference of 100 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.00 m. After traveling through 180 degree and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 100 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.00 h.

Show transcribed image text A certain commercial mass spectrometer (see Sample Problem 28 - 3) is used to separate uranium ions of mass 3.92 times 10 - 25 kg and charge 3.20 times 10 - 19 C from related species. The ions are accelerated through a potential difference of 100 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.00 m. After traveling through 180 degree and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 100 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.00 h.

Question
Other
asked 2020-11-26
Show transcribed image text A certain commercial mass spectrometer (see Sample Problem 28 - 3) is used to separate uranium ions of mass 3.92 times 10 - 25 kg and charge 3.20 times 10 - 19 C from related species. The ions are accelerated through a potential difference of 100 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.00 m. After traveling through 180 degree and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 100 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.00 h.

Answers (1)

2020-11-27
a) The magnitude of the manetic field is solvable using theequation \(\displaystyle{r}={m}\times\frac{{V}}{{{\left|{q}\right|}\times{B}}}\) , where r is the radius of theion's motion, m is the ion's mass, V is the ion's velocity, q isthe ion's charge, and B is the magnetic field acting on theion.
\(\displaystyle{\frac{{{1}}}{{{2}}}}{M}{\left({V}{e}{l}{o}{c}{i}{t}{y}\right)}^{{{2}}}={q}{\left({V}{o}{<}{a}\ge\right)}\)</span>
PSK\frac{1}{2}\times (3.92\times 10^{-25}kg) \times V^{2} = (3.2 \times 10^{-19} C) \times 100kVZSK
\(\displaystyle{V}={4.04}\times{10}^{{{5}}}\frac{{m}}{{s}}\)
\(\displaystyle{r}={m}\times\frac{{V}}{{{\left|{q}\right|}\times{B}}}\)
\(\displaystyle{1}{m}={\frac{{{\left({3.92}\times{10}^{{-{25}}}{k}{g}\right)}\times{4.04}\times{10}^{{{5}}}\frac{{m}}{{s}}}}{{{\left({3.2}\times{10}^{{-{19}}}{C}\times{B}\right)}}}}\)
B = 2.02Tesla
b) Since current is measured in coulombs per second, the totalcharge moved per hour is the mass per hour over the mass per ion(which gives us the number of ions per hour), multiplied by thecharge per ion. This value is then divided by 3600seconds (perhour) to attain the current.
(massCollected / massPerIon) * CoulombPerIon / TimePeriod= Current
\(\displaystyle{\frac{{{\left\lbrace{.1}\times{10}^{{-{3}}}{k}{g}\right\rbrace}{\left\lbrace{3.92}\times{10}^{{-{25}}}{k}{g}\right\rbrace}}}{\times}}{\frac{{{\left\lbrace{3}\times{10}^{{-{19}}}{C}\right\rbrace}{\left\lbrace{3600}{s}\right\rbrace}}}{=}}{I}\)
I = .0227Amps
c) Energy dissipated in the cup is just a function of the kineticenergy dissipated for each ion times the number of ions collectedduring the period.
PSK\frac{1}{2}M(Velocity)^2 \times (massCollected / massPerIon)= EnergyDisspated \frac{1}{2} \times \frac{1}{2} \times (3.92\times 10^{-25}kg) \times (4.04\times 10^{5})^{2} \times \frac{.1\times 10^{-3}kg}{3.92\times 10^{-25}kg}) = EnergyZSK
Energy = \(\displaystyle{8.16}\times{10}^{{{9}}}{J}{o}\underline{{e}}{s}\)
0

Relevant Questions

asked 2021-04-25
The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius \(\displaystyle{R}={7.4}\times{10}^{{-{15}}}\) m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
A. Find the radii of the two "daughter" nuclei of charge+46e.
B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.
C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit \(\displaystyle={1.66}\times{10}^{{-{27}}}\) kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes).
asked 2021-02-27
An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of \(\displaystyle{6.64}\cdot{10}^{{-{27}}}\) kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.10 T magnetic field.
A) What is the diameter of the path followed by this alpha particle?
B) What effect does the magnetic field have on the speed of the particle?
C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field?
D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?
asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
asked 2021-04-25
A wagon with two boxes of Gold, having total mass 300 kg, is cutloose from the hoses by an outlaw when the wagon is at rest 50m upa 6.0 degree slope. The outlaw plans to have the wagon roll downthe slope and across the level ground, and then fall into thecanyon where his confederates wait. But in a tree 40m from thecanyon edge wait the Lone Ranger (mass 75.0kg) and Tonto (mass60.0kg). They drop vertically into the wagon as it passes beneaththem. a) if they require 5.0 s to grab the gold and jump out, willthey make it before the wagon goes over the edge? b) When the twoheroes drop into the wagon, is the kinetic energy of the system ofthe heroes plus the wagon conserved? If not, does it increase ordecrease and by how much?
asked 2021-05-04
Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle. The ball is accelerated uniformly from rest to 10.0 m/s in 0.350 s, at which point it is released. Calculate (a) the angular acceleration of the arm, and (b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.
asked 2021-03-30
A long, straight, copper wire with a circular cross-sectional area of \(\displaystyle{2.1}{m}{m}^{{2}}\) carries a current of 16 A. The resistivity of the material is \(\displaystyle{2.0}\times{10}^{{-{8}}}\) Om.
a) What is the uniform electric field in the material?
b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?
c) What is the displacement current density in the material in part (b)?
d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?
asked 2021-02-19
An electric heater is used to heat a room of a volume \(\displaystyle{62}{m}^{{3}}\). Air is brought into the room at \(\displaystyle{5}^{\circ}\) C and is changed completely twice per hour. Heat loss through the walls amounts to approximately 850 kcal/h. If the air is to be maintainedat \(\displaystyle{20}^{\circ}\) C, what minimum wattage must the heater have? (The specific heat of air is about 0.17 kcal/kg*Co.)
asked 2021-02-21
How do you solve this problem? I don' t even know whereto begin.
A Ferrari with a mass of 1400 kg approaches a freeway underpassthat is 10 m across. At what speed must the car be moving, inorder for it to have a wavelength such that it might somehow"diffract" after passing through this "single slit"? How dothese conditions compare to normal freeway speeds of 30m/s?
asked 2021-02-14
The plane of a rectangular coil, 5.0-cm by 8.0-cm, is perpendicular to the direction of a magnetic field "B". If the coil has 75 turns and a total resistance of 8.0 Ohms, at what rate must the magnitude of "B" change to induce a current of 0.10 amps in the windings of the coil?
asked 2021-02-14
Mg reacts with H+ (aq) according to
\(\displaystyle{M}{g{{\left({s}\right)}}}+{2}{H}+{\left({a}{q}\right)}\to{M}{g}_{{2}}+{\left({a}{q}\right)}+{H}_{{2}}{\left({g}\right)}\)
Suppose that 0.524 g of Mg is reacted with 60.o ml of 1.0 M H+(aq). Assume that the density of the H+ (aq) solution os 1.00 g/ml,and that its specific heat capacity equals that of water. Theinitial and final temperatures are 22.0 degree celsius and 65.8degree celsius.
a) Is the reaction endothermic or exothermic?
b) Calculate \(\displaystyle\triangle{H}\) of of th reaction. Use correct sigs andgive units.
c) Calculate the \(\displaystyle\triangle{H}\) of the reaction per mole of magnesium.
...