Question

In: Physics

Elements that appear in the same column of the periodic table often share similar chemical properties....

Elements that appear in the same column of the periodic table often share similar chemical properties. In the case of the alkaline earth metals, this is troublesome since the body treats calcium (necessary for proper bone growth) and radium (a radioatictive element) as chemically similar, storing both in bone marrow. The radium then bombards nearby bone cells with alpha particles, causing them to \"crumble.\" Radium poisoning investigations often center on the identification of radium and its isotopes in bone samples using a mass spectrometer. Pictured is a schematic of a simplified mass spectrometer, showing the paths of calcium, barium (another alkaline earth metal) and radium isotopes entering the chamber. The region shown is immersed in a constant magnetic field of 0.352 T pointing out of the plane of the schematic. Motion of the positively-charged isotopes toward the right was initiated by a potential difference of 3082 V on the two plates shown. Using the data shown in the table below, calculate the path radius of the Ca ion.

Solutions

Expert Solution


1.) F=ma

2.) a=m*(v^2/r)

Substitute 2 into 1.

F=m*(v^2/r)

What is the force of a charge particle?


F=qVB => call this equation 3 and substitute into equation 1.

qvB=m*(v^2/r)

v's on both sides, and cancels out.

qB=m*(v/r)


We need to find v, so how do we find v?


A voltage was applied which accelerated the Ca ion. The voltage*charge of the ion gives us the potential energy lost and the amount of KE of the Ca ion. So, PE=q*V and KE=1/2mv^2, equate to each other and solve for v:


qV=1/2mv^2

sqrt*[2*qV/m]=v <= call this equation 4 and substitute it into are already substituted equation 1.  


qB=m*(sqrt*[2*qV/m]/r)

Now, we have to rearrange this equation and solve for r:


(qB/m)^2=[2*qV/m]/r)


r=[2*qV/m]/(qB/m)^2

Where

q=1.602 × 10^-19 C.
V=3082 V
m=40.1amu*(1.661 × 10^-27 kg/1 amu)=6.661 x 10^-26 kg  
B=0.352 T
and  
r=?

Solve for r:

r=[2*1.602 × 10^-19 C*3082 V/6.661 x 10^-26 kg]/(1.602 × 10^-19 C*0.352 T/6.661 x 10^-26 kg )^2

r=0.0205m


Related Solutions

Elements that appear in the same column of the periodic table often share similar chemical properties....
Elements that appear in the same column of the periodic table often share similar chemical properties. In the case of the alkaline earth metals, this is troublesome since the body treats calcium (necessary for proper bone growth) and radium (a radioactive element) as chemically similar, storing both in bone marrow. The radium then bombards nearby bone cells with alpha particles, causing them to "crumble." Radium poisoning investigations often center on the identification of radium and its isotopes in bone samples...
In the periodic table of the elements, only a few of the elements are gases at...
In the periodic table of the elements, only a few of the elements are gases at standard temperature and pressure. Those elements include the noble gases some of the halogens, and a few of the elements next to them, i.e. oxygen and nitrogen. So why are these elements gases?
The metals Cadmium and Mercury are similar in their chemical properties, but in terms of their...
The metals Cadmium and Mercury are similar in their chemical properties, but in terms of their absolute entropy at room temperature and pressure, they are very different. Why?
The Periodic Table of Elements is an organized table that contains all of the elements known-to-date....
The Periodic Table of Elements is an organized table that contains all of the elements known-to-date. How the Periodic Table developed and what are its key features? What will happen if new elements are discovered in the future? Be specific with your explanation. In other words, how a new element will be added to the periodic table.
4. Which two electron configurations represent elements that would have similar chemical properties? (1) 1s22s22p4       (2)...
4. Which two electron configurations represent elements that would have similar chemical properties? (1) 1s22s22p4       (2) 1s22s22p5       (3) [Ar]4s23d5       (4) [Ar]4s23d104p5 A) (1) and (2) B) (1) and (3) C) (2) and (3) D) (2) and (4) E) (3) and (4) 5. Which of the following make an isoelectronic pair: Cl–, O2–, F, Ca2+, Fe3+? A) Ca2+ and Fe3+ B) O2– and F C) F and Cl– D) Cl– and Ca2+ E) None of the above. 6. Which of the...
Describe the trends in properties for the elements belonging to Group VI A in the periodic...
Describe the trends in properties for the elements belonging to Group VI A in the periodic table. How do the following properties vary down the group? a. Atomic Radius b. 1st Ionization Energy c. Electron Affinity d. Oxidation number e. Electronic Configuration starting from the preceding noble gas configuration
The development of the periodic table and the elucidation of the trends and properties of its...
The development of the periodic table and the elucidation of the trends and properties of its elements spanned many decades. Now we can use it to predict the properties and reactivity of elements based only on their location in the periodic table. Let's practice some applications of this. A) Describe the size difference between chlorine and fluorine. Explain why they are different. B) If an atom has a high ionization energy(IE), like chlorine, what does that mean electronically, i.e., why...
The development of the periodic table and the elucidation of the trends and properties of its...
The development of the periodic table and the elucidation of the trends and properties of its elements spanned many decades. Now we can use it to predict the properties and reactivity of elements based only on their location in the periodic table. Let's practice some applications of this. A) Describe the size difference between chlorine and fluorine. Explain why they are different. B) If an atom has a high ionization energy(IE), like chlorine, what does that mean electronically, i.e., why...
Which of the following describes an atom or group of atoms that has similar chemical properties...
Which of the following describes an atom or group of atoms that has similar chemical properties when it occurs in different compounds? A. functional group B. isomer C. isotopes D. hydrocarbons
why trends appear across the period and down the group of the periodic table explain and...
why trends appear across the period and down the group of the periodic table explain and give the example
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT