Question

The figure (figure 1)is a graph of |ψ(x)|2 for an electron.

Answer 1

The value of "a" is found to be 0.5 nm^-1, and the probability of finding the electron between x = 1.0 nm and x = 2.0 nm is 0.25 or 25%, as calculated based on the area of the corresponding triangle in the graph.

Find the value of a and the probability of finding the electron between x = 1.0 nm and x = 2.0 nm:

Finding the value of a:

Recognize the shape: The graph is a triangle.

Recall the area formula for a triangle: Area = (base * height) / 2

Identify the base and height: In this case, the base of the triangle is 2 nm (from -1 nm to 1 nm on the x-axis) and the height is "a" (the vertical axis is not labeled, but we are asked to find the value of a).

Relate the area to the probability: The total area under the curve must be equal to 1, because the probability of finding the electron somewhere must be 100%.

Set up the equation: (2 nm * a) / 2 = 1

Solve for a: a = 1 / (2 nm) = 0.5 nm^-1

Finding the probability between x = 1.0 nm and x = 2.0 nm:

Identify the relevant area: We are interested in the area of the triangle between x = 1.0 nm and x = 2.0 nm.

Recognize the shape: This part of the graph is also a triangle.

Calculate the base and height of the smaller triangle: The base is 1 nm (from 1 nm to 2 nm on the x-axis) and the height is still "a" (0.5 nm^-1).

Calculate the area of the smaller triangle: (1 nm * 0.5 nm^-1) / 2 = 0.25

Interpret the result: The area of the smaller triangle represents the probability of finding the electron between x = 1.0 nm and x = 2.0 nm. Therefore, the probability is 0.25 or 25%.

Complete question:

The figure (figure 1)is a graph of |ψ(x)|2 for an electron. what is the value of a?What is the probability that the electron is located between x = 1.0 nm and x = 2.0 nm??

Answer 2

The value of `a` is
`0.5 nm^-1`.

The probability of finding the electron between x = 1.0 nm and x = 2.0 nm is 0.25.

1. Find the value of `a`:

The graph is a triangle with a base of 2 nm and a height of `a`.

The area of a triangle is (base * height) / 2.

The total area under the graph must be 1, so:

(2 nm * `a`) / 2 = 1

`a` = 1 / (2 nm) = 0.5 nm^-1

2. Find the probability between x = 1.0 nm and x = 2.0 nm:

The area of the triangle between x = 1.0 nm and x = 2.0 nm is a right triangle with a base of 1 nm and a height of `a`.

The area of this triangle is (base * height) / 2 =
`(1 nm * 0.5 nm^(-1)) / 2 = 0.25`

This area represents the probability of finding the electron between x = 1.0 nm and x = 2.0 nm, so the probability is 0.25.

Complete the question:

The figure (figure 1)is a graph of |ψ(x)|2 for an electron. what is the value of a?What is the probability that the electron is located between x = 1.0 nm and x = 2.0 nm??