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**1. Homework Statement**

A polonium nucleus of atomic number 84 and mass number 210 decays to a nucleus of lead by the emission of an alpha particle of mass 4.0026 atomic mass units and kinetic energy 5.5 MeV. (1 atomic mass unit=931.5 MeV/c^2=1.66x10^-27kg.) The atomic number of the lead nucleus is 82. The mass number of the lead nucleus is 205.9974 atomic mass units.

a) Determine the mass difference between the polonium nucleus and the lead nucleus, taking into account the kinetic energy of the alpha particle but ignoring the recoil energy of the lead nucleus.

b) Determine the speed of the alpha particle. A classical (nonrelativisitc) approximation is adequate.

**2. Homework Equations**

I think these are the equations necessary.

a) E=mc^2

b) KE= (1/2)mv^2

**3. The Attempt at a Solution**

a) I rearranged E=mc^2 so m=E/c^2

5.5 MeV/ (3x10^8 m/s)= 6.11x10^-17 MeV/ (m/s)^2

Next, I converted to kg.

(5.5MeV/c^2)(1.66x10^-27 kg/931.5 MeV/c^2)=

**1.78x 10^-30 kg**

b) I rearranged KE=(1/2)mv^2 for v^2=2KE/m

KE=931.5 MeV, m=4.0026 amu

Then I took the square root and got v=21.57 m/s.

I know what I did is completely wrong, but it was the best I could figure out. Help would be greatly appreciated.