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Chapter 41: Q. 4 (page 1206)

A hydrogen atom has orbital angular momentum $3.65 脳 10^{- 34} J s$
a. What letter $(s, p, d o r f)$ describes the electron?
b. What is the atom鈥檚 minimum possible energy? Explain.

Short Answer

Expert verified

a. The electron is $L = 3$ .

b. The atom鈥檚 minimum possible energy is $- 0.850 e V$

Step by step solution

01

Part (a) step 1: Given Information

We need to describe the electron letter is $(s, p, d o r f)$ .

We have given angular momentum is $3.65 脳 10^{- 34} J s$ .

02

Part (a) step 2: Simplify

Finding orbital angular momentum is:

$L = \sqrt{l (l + 1)} 魔$

$\frac{L}{魔} = \frac{\sqrt{l (l + 1)} 魔}{魔}$ (Divide both sides by $h$ ) $\begin{array}{r} \frac{L}{魔} & = \sqrt{l (l + 1)} \\ {(\frac{L}{魔})}^{2} & = {(\sqrt{l (l + 1)})}^{2} \\ {(\frac{L}{魔})}^{2} & = l (l + 1) \end{array}$

${(\frac{(3.65 脳 10^{- 34} J s)}{(1.5 脳 10^{- 34} J s)})}^{2} = l (l + 1) \begin{matrix} 12.08 = l (l + 1) \\ 鈬� l = 3 \end{matrix}$

03

Part (b) step 1: Given Information

We need to find the atom鈥檚 minimum possible energy.

04

Part (a) step 2: Simplify

Finding the atom minimum energy is :

$E_{m i n} = - \frac{13.60 e V}{n^{2}} (w h e r e n = 4) E_{m i n} = - \frac{13.60 e V}{4^{2}} E_{m i n} = - \frac{13.60 e V}{16} E_{m i n} = - 0.850 e V$

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Most popular questions from this chapter

A neon discharge tube emits a bright reddish-orange spectrum, but a glass tube filled with neon is completely transparent. Why doesn鈥檛 the neon in the tube absorb orange and red wavelengths?

In FIGURE Q $41.12,$ a photon with energy $2.0 e V$ is incident on an atom in the $p$ state. Does the atom undergo an absorption transition, a stimulated emission transition, or neither? Explain.

a. What is the decay rate for the $2 p$ state of hydrogen?

b. During what interval of time will $10 %$ of a sample of $2 p$ hydrogen atoms decay?

A sodium atom emits a photon with wavelength $818 n m$ nm shortly after being struck by an electron. What minimum speed did the electron have before the collision?

Does each of the configurations in FIGURE Q $41.6$ represent a possible electron configuration of an element? If so,

(i) identify the element and

(ii) determine whether this is the ground state or an excited state. If not, why not?

See all solutions

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