hey again...got another physics question i need some help with (or help making sure i am actually getting the right answer).....

 

The light isotope of lithium, 5Li, is unstable and breaks up into a proton (hydrogen nucleus) and an α particle (helium nucleus). In this process, a total of 3.15 x 10-13 J is released, appearing as the kinetic energy of the two reaction products. Determine the velocities of the proton and α particle that arise from the decay of a 5Li nucleus at rest. ( Note: The masses of the proton and alpha particle are

mp = 1.56 x 10-27 kg and mα = 4mp = 6.68 x 10-27 kg.)

 

 

i am working on it now, but i thought i'd give peoples the heads up first... i will post my attempt at a solution in a bit...

 

Cheers

Sarah

lol its a lot of working so i won't write it all out here just yet.... but the gerneral gist i think is that you use

 

initial momentum = final momentum

ie. m1v1 = m2v2

 

and that KEf = PEi

ie. .5*m1*v1^2 + .5*m1*v2^2 = 3.15 x 10-13 J

 

and using the second equation there you get the v2 in terms of v1, then sub it into the first equation (momentum one) and get a numerical answer for v1. It is then easy to also compute v2.

 

so after doing this i get.

 

Velocity of proton (hydrogen nucleus) = 2.32 x 10^7 m/s

and

Velocity of alpha particle = -5.80 x 10^6 m/s

 

Sarah...

only thing is i used mass of alpha particle = 4 x proton mass

 

but i dunno in the question it says that

mp = 1.56 x 10-27 kg and mα = 4mp = 6.68 x 10-27 kg

 

but 4 x 1.56 = 6.24 !!!! not 6.68???

 

well anywho...what do you guys think?

actually i redid it because i mistyped the question and the protons mass should be

1.67 x 10^-27 kg

 

so i now get

 

Velocity of Proton = 7.94 x 10^-7 m/s

and

Velocity of Alpha Particle = -1.98 x 10^-7 m/s

 

sorry if i didnt show complete working but i am in a really really big rush so can someone tell me if this is right?

 

cheers and thanks

 

Sarah :)

lol

 

sorry sorry!!!

 

after a good night sleeping on it....i have changed my answers and this time i know i'm right (...well i hope so anyways )

 

I get

Velocity of proton (hydrogen nucleus) = 1.74 x 10^7 m/s

and

Velocity of alpha particle = -4.34 x 10^6 m/s

lol just thought i'd make it clear hehe

so can someone tell me if this is right?

I ended up getting

 

[math]v_p\approx1.737228848 \cdot 10^7[/math][math]m/s[/math]

[math]v_\alpha\approx-4.34307212 \cdot 10^6[/math][math]m/s[/math].

 

Where [math]v_p[/math] is the velocity of the proton, and [math]v_\alpha[/math] is the velocity of the alpha particle.

 

Of course,

 

[math]v_p\approx-1.737228848 \cdot 10^7[/math][math]m/s[/math]

[math]v_\alpha\approx4.34307212 \cdot 10^6[/math][math]m/s[/math]

 

is correct as well.

lol cool thanks Dap thats what i ended up getting too lol after a long time !