A mercury nucleus contains 201 nucleons (80 protons and 121 neutrons) packed tig

Question

A mercury nucleus contains 201 nucleons (80 protons and 121 neutrons) packed tightly against each other. A single nucleon (proton or neutron) has a radius of about 1 times 10^-15 m. Remember that the volume of a sphere 4/3 pi r^3. (a) Calculate the approximate radius of the mercury nucleus. 5.86e-15 m (b) Calculate the approximate radius of the alpha particle, which consists of 4 nucleons, 2 protons and neutrons. 1.59e-15 m (c) What kinetic energy must alpha particles have in order to make contact with a mercury nucleus? MeV

Explanation / Answer

c) when alfa partcile comes to contact mercury necleus,

the distance between centers, d = (5.86 + 1.59)*10^-15

= 7.45*10^-15 m

Q_mercury = 80*e

Q_alfa = 2*e

Apply conservation of energy

initial kinetic energy of alfa particle = final elctric potential energy

KEi = k*Q_mercury*Q_alfa/d

= 9*10^9*80*1.6*10^-19*2*1.6*10^-19/(7.45*10^-15)

= 4.948*10^-12 J

= 4.948*10^-12/(1.6*10^-19) eV

= 3.09*10^7 eV

= 30.9 MeV

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