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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

$1.0 脳 10^{6}$ atoms are excited to an upper energy level at $t = 0 s$ . At the end of $20 n s$ , $90 %$ of these atoms have undergone a quantum jump to the ground state.

a. How many photons have been emitted?

b. What is the lifetime of the excited state?

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 localid="1649073297418" $n = 6$ state. The selection rule for the rigid box allows only those transitions for which $鈭� n$ 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?

An excited state of an atom has a $25 n s$ lifetime. What is the probability that an excited atom will emit a photon during a $0.50 n s$ interval?

The $5 d 鈫� 3 p$ transition in the emission spectrum of sodium has a wavelength of $499 n m$ .What is the energy of the $5 d$ state ?

A hydrogen atom is in the $2 p$ state. How much time must elapse for there to be a $1.0 %$ chance that this atom will undergo a quantum jump to the ground state?

See all solutions

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