Finding the kinetic energy of an Alpha Particle

[pdinemcm]

Can anyone help with this problem? I think the solution may be simpler than I'm trying to make it.

Colin measured the speed of an alpha particle that was emitted from a U-238 nucleus to be 2.20x10^8 m/sec. Calculate the kinetic energy of the alpha.

Is all you need the equation KE = 1/2 m*v^2 ??

Thank you!

 

[sam_021]

are u ignoring relativistic effect? if so then yes that's all u do

 

[Munnkeyman]

Can anyone help with this problem? I think the solution may be simpler than I'm trying to make it.

Colin measured the speed of an alpha particle that was emitted from a U-238 nucleus to be 2.20x10^8 m/sec. Calculate the kinetic energy of the alpha.

Is all you need the equation KE = 1/2 m*v^2 ??

Thank you!

Homework Statement

Homework Equations

The Attempt at a Solution

As sam_021 said, you have neglected relativistic effects.
You have nearly answered your own question.
In your post click on "kinetic energy"
When you look at the speed of the alpha particle

$$v\ = \ 2.20\ x\ 10{^8} m/s$$

$$This\ speed\ is\ \approx \ \frac{2}{3}\ c\$$

This is a significant fraction of the speed of light, therefore you should use the formula
for relativistic linear motion, as below.

$$KE\ =\ \frac{mc^2}{\sqrt{1\ -\ v^2/c^2}}-mc^2\ \$$

So use

$$m\ =\ 6.644\ \ 656\ \ 20 \ \ x \ \ 10{^\ -27} \ \ Kg\ \ or \ \ 3.727 \ \ 379 \ \ 109 \ \ GeV/c^2$$
$$v\ = \ 2.20\ x\ 10{^8}\ \ m/s$$
$$c\ = \ 2.997\ \ 924\ \ 58 \ \ x \ \ 10{^8}\ \ m/s$$

And you'll get your answer.

 

[SteamKing]

The exponent in the mass of the alpha particle should be -27 in Post #3.

 

[Munnkeyman]

The exponent in the mass of the alpha particle should be -27 in Post #3.

Correct, a syntax error with TeX. Thanks for spotting it.