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Chapter 41: Q.44 (page 1208)

Three electrons are in a one-dimensional rigid box (i.e., an infinite potential well) of length $0.50 n m$ . Two are in the n = 1 state and one is in the n = 6 state. The selection rule for the rigid box allows only those transitions for which n is odd.
a. Draw an energy-level diagram. On it, show the filled levels and show all transitions that could emit a photon.
b. What are all the possible wavelengths that could be emitted by this system?

Short Answer

Expert verified

274.88 nm is the short answer of this question.

Step by step solution

01

E2=h28ml2Rigid box:

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Most popular questions from this chapter

$1.0 \times 10^{6}$ sodium atoms are excited to the $3 p$ state at $t = 0$ s. How many of these atoms remain in the $3 p$ state at

(a) $t = 10 n s$

(b) $t = 30 n s$ , and

(c) $t = 100 n s$ ?

Suppose you have a machine that gives you pieces of candy when you push a button. Eighty percent of the time, pushing the button gets you two pieces of candy. Twenty percent of the time, pushing the button yields $10$ pieces. The average number of pieces per push is $N_{a v g} = 2 \times 0.80 + 10 \times 0.20 = 3.6$ . That is, $10$ pushes should get you, on average, $36$ pieces. Mathematically, the average value when the probabilities differ is $N_{a v g} = \sum (N_{i} \times P r o b a b i l i t y o f i)$ . We can do the same thing in quantum mechanics, with the difference that the sum becomes an integral. If you measured the distance of the electron from the proton in many hydrogen atoms,

you would get many values, as indicated by the radial probability density. But the average value of $r$ would be

$r_{a v g 0} = \int_{0}^{\infty} r P_{r} (r) d t$

Calculate the average value of $r$ in terms of $a_{B}$ for the electron in the $1 s$ and the $2 p$ states of hydrogen.

Shows that the ionization energy of cadmium $(z = 48)$ is larger than that of its neighbors. Why is this?

Show that $h c = 1240 e V n m$ .

Draw a series of pictures, similar to the ground states of $K, S c, C o$ and $G e$ .

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