Question

A Barium nucleus with a charge 56 and a Krypton nucleus with a charge 36 fly apart from rest at an initial separation of 8 fm (8 x 10-15m). How much kinetic energy do the two nuclei share when they are far apart?

A) 900 eV

B) 1.8 MeV

C)235 KeV

D)360 MeV

E)4.5x10^20 eV

Answer 1

Concept - the initial potential energy converts to kinetic energy when they are far apart. So, the kinetic energy is equal to initial potential energy,

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Answer 2

Calculation:

1. Key Concepts:

• Initial potential energy (U_initial) between the two nuclei is converted entirely into kinetic energy (K_final) when they are far apart (since they start from rest).

• Coulomb potential energy formula:

  $$U=\frac{k{q}_1{q}_2}{r}$$

  Where:

• (Coulomb's constant),

• $q_1=56e$, $q_2=36e$ (charges of Barium and Krypton nuclei),

• $e=1.6\times 10^{-19}\text{C}$ (elementary charge),

• $r=8\times 10^{-15}\text{m}$.

2. Calculate Potential Energy (U_initial):

$$U=\frac{(8.99\times 10^9)\times (56\times 1.6\times 10^{-19})\times (36\times 1.6\times 10^{-19})}{8\times 10^{-15}}$$

Simplify:

$$U=\frac{8.99\times 10^9\times 56\times 36\times (1.6\times 10^{-19}{)}^2}{8\times 10^{-15}}$$$$U=\frac{8.99\times 56\times 36\times 2.56\times 10^{-29}}{8\times 10^{-15}}$$$$U=\frac{4.64\times 10^{-25}}{8\times 10^{-15}}=5.8\times 10^{-11}\text{J}$$

3. Convert Joules to Electron-Volts (eV):

$$1\text{eV}=1.6\times 10^{-19}\text{J}⟹K=\frac{5.8\times 10^{-11}}{1.6\times 10^{-19}}=3.625\times 10^8\text{eV}$$$$K=362.5\text{MeV}\approx 360\text{MeV}$$

 

Answer:

The correct answer is D) 360 MeV.