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N Netflix e x V c physics question ICF x Mastering Physics: As x MasteringPhysics: HC x C fi https: masteringphysics.com/myct/itemView assignment ProblemID D*62247992 Apps M UCR PCC f Facebook o My subscriptions Twitter welcome, Kurt LancerPoint Logir NBA.com finding the name vy WebAssign LOG E LeBrown James S Slicethepie i Time Warner Cab PHYS 40c, Spring 2016 Homework 03 Problem 28.53 Problem 28.53 Part A A proton is fired from far away toward the nucleus of a mercury atom. Mercury is element number the proton is fired at a speed of 4.6x107 m/s what is its closest approach to the surface of the nucleus? Assume the nucleus remains at rest 80. and the diameter of the nucleus is 14.0 fm. Express your answer totwo significant figures and include the appropriate units. d J 6.79 Submit My Answers Giv incorrect: Try Again: 4 attempts remaining O Ask me anything Kurt G1 Other bookmarks Signed in as Kurt Tomongin l Hep Cose previous I 12 of 14 l next Provide Feedback Continue 2:43 PM 4/19/2016

Explanation / Answer

From the law of conservation of energy the kinetic energy of the proton is converted into the potential energy at the point of nearest distance from the nucleus at this closest distance the the velocity of proton is zero

Intial Kinetic energy = Potential energy

when the proton at the closest position the potential energy is =k q(zq) / r

here q is the charge of proton and z is the atomic number of mercury

(1/2) m v2 = k q(zq) / r

and r =(2kzq2) /(mv2)

here q =1.60 x10-19 C ,z =80 , m =mass of proton =1.67x10-27 kg , v=velocity of proton =4.6x107 m/s

k =9.0 x109 Nm2/C2

r =(2x 9.0 x109 Nm2/C2 x 80 )(1.60 x10-19 C)2 / [(1.67x10-27 kg )(4.6x107 m/s)2]

r = 10.43 x10-15 m =10.43 fm (closest distance from the center of nucleus)

the closest distance from the surface = r -radius of nucleus

here radius of the nucleus given as = (14.0 fm) =7.0 fm

the closest distance from the surface = 10.43 fm -7.0fm =3.43 fm

therefore the closest distance from the surface is 3.43 fm

  

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