# Help needed following my notes - Probability protons will penetrate Coulomb barrier

## Homework Statement

There isn't an exact problem I'm struggling with, it's one small part of a larger problem, which involves finding the probability protons will penetrate the Coulomb barrier.

I'm trying to understand an example in my notes, and the bit that confuses me is attached as an image file.

## Homework Equations

The equation is shown in the attachment, and I know it's correct.

Probability = exp [ (- (EG/E)) ^ 0.5]

## The Attempt at a Solution

Basically what I don't understand is simple - how the answer was found using the formula.

EG (Gamow energy) is 493 kev, E is 2 ev, but when those are subbed into the formula, my notes say you should get 1.5 x 10 ^ 7.

When I try to work it out on my calculator, it says error.

I firstly divide - EG/E, get a negative number = - 246.5
Then I try to put it to the power of a half (same as taking the square root) and I can't, because it's a minus number. I know you can't perform that operation with a minus number.
And then you're supposed to take the exponential, but I havent managed to put it to the power of a half yet!

How on earth does this formula work? The number you're trying to put to the power of a half is always going to be negative! :(

I'm stumped!

Hope the attachment works okay, thank you for any help.

#### Attachments

• whatdoesthismean.jpg
7.6 KB · Views: 378

Apologies, I've solved it!

If anyone wants to know the solution:

With that kind of equation, you're supposed to divide first, THEN put it to the power of a half, THEN add in the minus sign, THEN take the exponential.

Sorry guys!