An Alpha Particle (A Helium Nucleus, Having Charge $+ 2 e$

Multiple Choice

An alpha particle (a helium nucleus, having charge $+ 2 e$ and mass $6.64 \times 10 ^ { - 27 } \mathrm {~kg}$ ) moves head-on at a fixed gold nucleus (having charge $+ 79 e$ ) . If the distance of closest approach is $2.0 \times 10 ^ { - 10 } \mathrm {~m}$ , what was the speed of the alpha particle when it was very far away from the gold? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = \right.$ $\left. 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $2.3 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
B) $4.6 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
C) $2.3 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
D) $4.6 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$