Question

What is the value of the constant a in FIGURE Q39.5?

Short answer

a = 2mm^-1

Step-by-step solution

Given parameters

A graph of probability density of a particle.

the graph forms a triangle with base length of 1mm (from 1mm to 2mm)

and height of a.

Finding a

Now we know that probability of finding the particle from $-\infty to+\infty$is 1.

And here all the probability density is distributed from x= 1mm to x = 2mm.

So probability of finding the particle between 1mm to 2mm is 1.

this means integral of this wave function from 1mm to 2mm will give 1.

And integral of a function also tells about area under the graph.

$\Rightarrow areaofthisgraph=1$

$$\begin{gathered} \Rightarrow areaofthetriangle=1 \\ \Rightarrow \frac{1}{2}\times 1mm\times a=1 \\ \Rightarrow a=2m{m}^{-1} \end{gathered}$$

Hence, the value of a is 2mm^-1