Item 8 Singly ionized (one electron removed) atoms are accelerated a.pdf
Is the set of all real-valued functions f that satisfy a vector space? Explain why or why not carefully Is the set of all real-valued functions f that satisfy (f(-1)^{2})-(f(1)^{^{2}})=0 a vector space? Explain why or why not carefully Solution We are given [ f ( - 1)2 ] - [ f ( 1)2 ] = 0 or, [ f ( - 1)2 ] = [ f ( 1)2 ] or , f (1) = f (1) [ since ( -1)2 = 1 and also (1)2 = 1] This is universally true for all the real valued functions f . including the function 0 . Let f and g be two functions which satisfy this condition. Then, we have ( f + g)( 1) = (f +g)( 1) or, [( f + g) ( - 1)2 ] = [( f + g) ( 1)2 ] or [( f + g) ( - 1)2 ] - [( f + g) ( 1)2 ] = 0 so that the sum of the functions satisfying the given condition also satisfies this condition. Further, if a is a scalar, then af (1) = af (1) or af(1) - af(1) = 0 or, [af ( - 1)2 ] - [ af ( 1)2 ] = 0 so that the function af also satisfies the given condition. Thus the set of all functions f, satisfying the condition [ f ( - 1)2 ] - [ f ( 1)2 ] = 0 is a vector space..
Item 8 Singly ionized (one electron removed) atoms are accelerated a.pdf
Is the set of all real-valued functions f that satisfy a vector space? Explain why or why not carefully Is the set of all real-valued functions f that satisfy (f(-1)^{2})-(f(1)^{^{2}})=0 a vector space? Explain why or why not carefully Solution We are given [ f ( - 1)2 ] - [ f ( 1)2 ] = 0 or, [ f ( - 1)2 ] = [ f ( 1)2 ] or , f (1) = f (1) [ since ( -1)2 = 1 and also (1)2 = 1] This is universally true for all the real valued functions f . including the function 0 . Let f and g be two functions which satisfy this condition. Then, we have ( f + g)( 1) = (f +g)( 1) or, [( f + g) ( - 1)2 ] = [( f + g) ( 1)2 ] or [( f + g) ( - 1)2 ] - [( f + g) ( 1)2 ] = 0 so that the sum of the functions satisfying the given condition also satisfies this condition. Further, if a is a scalar, then af (1) = af (1) or af(1) - af(1) = 0 or, [af ( - 1)2 ] - [ af ( 1)2 ] = 0 so that the function af also satisfies the given condition. Thus the set of all functions f, satisfying the condition [ f ( - 1)2 ] - [ f ( 1)2 ] = 0 is a vector space..
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Item 8 Singly ionized (one electron removed) atoms are accelerated a.pdf
- 1. Item 8 Singly ionized (one electron removed) atoms are accelerated and then passed through a velocity selector consisting of perpendicular electric and magnetic fields. The electric field is 158 V/m and the magnetic field is 3.13 Times 10^2 T. The ions next enter a uniform magnetic field of magnitude 1.73 Times 10^-2 T that is oriented perpendicular to their velocity. How fast are the ions moving when they emerge from the velocity selector? If the radius of the path of the ions in the second magnetic field is 17.4 cm, what is their mass? Solution A) In Velocity selector Electric field & Magnetic field forces on ions are equal & opposite ,this is because it allows ions with a particular velocity only passes undeflected. so we can say, Bqv = Eq B:magnetic field density E:Electric field v:velocity at which the ions remains undeflected. v=E/B v = 158V/m / 3.13*10-2 T => v = 4.78*103 m/s B) as it enteres next in uniform magnetic field of value B=1.73*10-2 T Work done in uniform magnetic field is zero.It only changes the direction.So B provides centripetal force for the ions while changing direction in circular path of radius r=17.4cm. Bqv = mv²/r m = Bqr / v = (1.73*10-2T)(1.6*10-19C)(0.174m) / (4.78*103m/s) =>m = 1*10-25 kg