Question

An electron is trapped in a one-dimensional infinite potential well in a state with quantum numbern = 17 . How many points of (a) zero probability and (b) maximum probability does its matter wave have?

Short answer

(a) The matter wave has 18 points of zero probability.

(b) The matter wave has 17 points of maximum probability.

Step-by-step solution

Given data

• The value of the principal quantum number is, n = 17 .

Significance of number of points of zero and maximum probability does a matter wave have

In this question, the number of points of zero probability that a matter wave have can be obtained by adding the number 1 to the principal quantum number. The number of points of maximum probability would be the same as the principal quantum number.

(a) Determination of the number of points of zero probability

The expression to calculate the number of points of zero probability that a matter wave has are-

${\left(N\right)}_0=n+1$

Here,${\left(N\right)}_0$ is the number of points of zero probability does its matter have.

Substitute all the known values in the above equation.

$$\begin{gathered} {\left(N\right)}_0=17+1 \\ =18 \end{gathered}$$

Thus, the number of points of zero probability that a matter wave has are 18 .

(b) Determination of the number of points of maximum probability

The expression to calculate the number of points of maximum probability that a matter wave has is written as,

${\left(N\right)}_{max}=n$

Here,${\left(N\right)}_{max}$ is the number of points of maximum probability does its matter have.

For the given values, the above equation becomes-

${\left(N\right)}_{max}=17$

Thus, the number of points of maximum probability that a matter wave has is 17 .