Chapter 41: Q. 4 (page 1206)

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

Short Answer

Expert verified

a. The electron is $L = 3$ .

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

Step by step solution

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 $3.65 \times 10^{- 34} J s$ .

Part (a) step 2: Simplify

Finding orbital angular momentum is:

$L = \sqrt{l (l + 1)} ħ$

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

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

Part (b) step 1: Given Information

We need to find the atom’s minimum possible energy.

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

Short Answer

Step by step solution

Part (a) step 1: Given Information

Part (a) step 2: Simplify

Part (b) step 1: Given Information

Part (a) step 2: Simplify

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A hydrogen atom has orbital angular momentum 3.65×10-34Jsa. What letter s,p,dorf describes the electron?b. What is the atom’s minimum possible energy? Explain.

Short Answer

Step by step solution

Part (a) step 1: Given Information

Part (a) step 2: Simplify

Part (b) step 1: Given Information

Part (a) step 2: Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Scientific Method Physics

Magnetism

Measurements

Thermodynamics

Engineering Physics

Study anywhere. Anytime. Across all devices.

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