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## Homework Statement

Alpha particle mass - 4amu

velocity alpha particle - 3.0x10^5m/s

^{197}Au Nucleus mass - 197amu

Head-on elastic collision. Find the final velocity of both the particles

## Homework Equations

Kinetic Energy conserved:

1/2m

_{1}v

_{1i}= 1/2m

_{1}v

_{1f}+ 1/2m

_{2}v

_{2f}

Momentum Conserved:

m

_{1}v

_{1i}= m

_{1}v

_{1f }+ m

_{2}v

_{2f}

## The Attempt at a Solution

For Momentum:

4 x (3 x 10^5) = 4V

_{1f}+ 197v

_{2f}

3 x 10^5 = V

_{1f}+ 49.25v

_{2f}

V

_{1f}= 3 x 10^5 - 49.25v

_{2f}

For Kinetic Energy

4 x (3.0 x 10^5)

^{2}= 4V

_{1f}

^{2}+ 197v

_{2f}

^{2}

3.6 x 10

^{11}= 4V

_{1f}+ 197v

_{2f}

9 x 10

^{10}= V

_{1f}+ 49.25v

_{2f}

Subbing in one for the other

9x 10

^{10}= (300,000 - 49.25v

_{2f})

^{2}+ 49.25v

_{2f}

The v

_{2f}and V

_{1f}values I get doesn't work out

Thanks in advance for your help.