The proabability density of an electron

[worries]

Homework Statement

The following is a graph of |(x)|^2

https://www.physicsforums.com/attachment.php?attachmentid=14887&d=1217540634

Question is.

What is the probability that an electron will be detected ina 0.0010-cm-wide region at x = 0.50 cm? At x= 0.999 cm?
b) If 10^4 electrons are detected, how many are expected to land in the interval -0.30 cm - 0.30 cm.

Also, let's suppose that this was a graph for the |(x)|^2 of a neutron.
How you you find the value 'a' if it wasn't given?

Homework Equations

I know that Probability of landing at x = (probability density at x )* (length)
Also know that expected value = number of electrons * probability.

But I am having trouble putting these two together. Can some please show me how to do this question?

The Attempt at a Solution

So I think the probability density at 0.50 cm is 0.5 cm^-1 (reading the graph, the slope is -1 so the y value seems to be 0.5 cm^-1)

So P(x) = 0.5 cm^-1* 0.0010 cm = 0.0005? But the answer is 0.005

And I have no idea how to find 'a' by using only the information from the graph.

Can someone help me with this whole concept?

 

[worries]

I meant graph of |psi (x)|^2

 

[dimeking]

I think your graph's horizontal axis should be labeled in cm.

The slope of your probability density function on the positive-x side is positive one.

To find a, you need to consider the integral of your (or any) probability function from negative infinity to positive infinity.