Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use Equation (5.16) to calculate the de Broglie wavelength of a $\mathrm{N}_{2}$ molecule at $300 \mathrm{K}$.

$2.76 \times 10^{-11} \mathrm{m}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Drexel University

University of Kentucky

Lectures

04:49

In chemistry and physics, electronic structure is the way the electrons of an atom are arranged in relationship to the nucleus. It is determined by the subshells the electrons are bound to, which are in turn determined by the principal quantum number ("n") and azimuthal quantum number ("l"). The electrons within an atom are attracted to the protons in the nucleus of that atom. The number of electrons bound to the nucleus is equal to the number of protons in the nucleus, which is called the atomic number ("Z"). The electrons are attracted to the nucleus by this mutual attraction and are bound to the nucleus. The electrons within an atom are attracted to each other and this attraction determines the electron configuration. The electron configuration is described by the term symbol, which is the letter used to identify each subshell.

16:45

In physics, the wave–particle duality is the concept that every object or process, no matter how large or how small, behaves as both a wave and a particle. The wave–particle duality is one of the central concepts in quantum mechanics.

02:12

Calculate the de broglie w…

01:29

Use the de Broglie relatio…

04:18

calculate the de broglie w…

01:07

01:00

Find the de Broglie wavele…

03:42

05:40

Calculate the de Broglie w…

02:50

02:00

Find an expression for the…

01:09

What is the de Broglie wav…

All right, So we're asked to use Equation 5.16 which is the root, mean square velocity equation. To find the de Broglie wavelength oven end to congestion, the dia nitrogen molecule. So we can go ahead and say that the root mean square velocity is equal to you. Square root three times the ideal gas constant in jewels Time Senator and Calvin divided by the molar mass in kilograms per mole is equal to plank's constant, divided by the mass of one molecule times wavelength. Okay, since we know that rooming square is velocity is going to be the velocity plug in the Debre uglies wavelength question. So putting this all together we get this square root, uh, three times 8.314 times 300 killed in all right, And the mass of one mole in terms of kilograms is just 28 grams, divided by thousands, 2.0 28 And with us from evil to Plank's constant, which is 6.63 times 10 to the negative. 34th Jules per second, right by the massive one Adam or one molecule into which we confined by dividing 28 grams per mole by the Dodgers number. So it comes out to 28. We're sorry. It comes out to be not 28. Ah, 4.65 times 10 to the negative. 26 kilograms. So we will say that 4.65 times 10 to the native 26th. And this is in. Remember, since seven kilograms, we divided this number right here. And kill grants, promote, abided by off Dodgers number and then the wavelength. So this is our variable. We're gonna go ahead and plug everything in the calculator. Solve it out. When you do, that wavelength comes out to be 276 nanometers or 2.76 times 10 to the negative 11th meters. This is the wavelength of die nitrogen molecule traveling Rumi Square velocity at 300 Kelvin.

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:23

Classify each of the following species as a weak or strong base: (a) LiOH, (…

02:21

Briefly describe what happens in an acid-base titration.

08:29

The explosive nitroglycerin $\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{N}_…

01:17

Does the addition of a catalyst have any effects on the position of an equil…

01:43

Why is it more convenient to predict the direction of a reaction in terms of…

03:28

At $850^{\circ} \mathrm{C}, \mathrm{CaCO}_{3}$ undergoes substantial decompo…

01:26

A $6.11-\mathrm{g}$ sample of a $\mathrm{Cu}-\mathrm{Zn}$ alloy reacts with …

The first four ionization energies of an element are approximately $579 \mat…

Use Le Châtelier's principle to explain why the equilibrium vapor press…

01:56

Identify the Maxwell speed distribution curves shown here with the following…