alpha decay

[Sarahisme]

Hi all.

 

i can't quite figure out how to modify the equation for this alpha particle decay stuff....any ideas ?

 

 

i think i need to modify this equation:

 

 

anyway, help would be great!

 

thanks guys & gals

 

Sarah

[swansont]

E_G is the energy of the ground state?

 

You have the tunneling probability for one strike against a barrier. If you have the energy of the alpha, you should be able to calculate how often it hits the barrier, and get the total probability of tunneling.

 

You can use the U-235 data to fix one parameter of your equation, and then estimate the Pu-239 half-life.

[Sarahisme]

oh E_G is Gamow energy

[Sarahisme]

E_G is the energy of the ground state?

 

You have the tunneling probability for one strike against a barrier. If you have the energy of the alpha' date=' you should be able to calculate how often it hits the barrier, and get the total probability of tunneling.

 

You can use the U-235 data to fix one parameter of your equation, and then estimate the Pu-239 half-life.[/quote']

 

 

but don't i have to change the equation because the current equation contains mu, which is the reduced mass?

 

sorry i should dexplain, ...initially this equation was for two protons colliding and possible fusing...

[swansont]

I think what you need is an equation that gives you the probability of tunneling through a barrier. (like this)

[Sarahisme]

hmm i am getting confused...

 

ok lets start from the begining....

 

we are given that

 

[math] \lambda = v \rho [/math]

 

then i think i need to somehow manipulate the equation in my first post...hmmmmm

[Sarahisme]

i am thinking that its something to do with this

 

 

 

but this involves 3D stuff, so i think i need to simplify it down...yeah?

[swansont]

That looks more like an equation for a potential well; you can probably do a 1-D model of it.

[Sarahisme]

how do i work out the Z number for U-235 and Pu-239?

[swansont]

That should be trivial to look up, but since I'm here: U has 92 protons, Pu has 94 and the alpha has two.

[Sarahisme]

k thanks, i got it now!

 

thanks for all your help btw!