/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 50 Neutron diffraction is used in d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 50

Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at \(1.00 \%\) of the speed of light. b. Calculate the velocity of a neutron with a wavelength of \(75 \mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{~m}\right)\)

Short Answer

Expert verified
a. The de Broglie wavelength of a neutron moving at 1% of the speed of light is approximately \(1.319 \times 10^{-13} m\). b. The velocity of a neutron with a wavelength of \(75 pm\) is approximately \(5.281\times10^4 m/s\).

Step by step solution

01

Part a: Calculate the de Broglie wavelength

To calculate the de Broglie wavelength, we first need the formula: \(位 = \dfrac{h}{mv}\) Where 位 is the de Broglie wavelength, h is Planck's constant (\(6.626 \times 10^{-34} Js\)), m is the mass of a neutron (\(1.675 \times 10^{-27}kg\)), and v is the velocity of the neutron. The velocity of the neutron is 1% of the speed of light, so we have to calculate that first: \(v = 0.01c\) Where c is the speed of light (\(3.00 \times 10^8 m/s\)) and 0.01 represents the 1% of the speed of light.
02

Calculate the velocity of the neutron

First, let's find the velocity of the neutron: \(v = 0.01\times(3.00 \times 10^8 m/s) = 3.00 \times 10^6 m/s\)
03

Compute the de Broglie wavelength

Now, we can use the given formula to calculate the de Broglie wavelength: \(位 = \dfrac{6.626 \times 10^{-34} Js}{(1.675\times10^{-27} kg)(3.00\times10^6 m/s)}\) \(位 = \dfrac{6.626 \times 10^{-34}}{5.025\times10^{-21}}\) \(位 = 1.319 \times 10^{-13} m\) Therefore, the de Broglie wavelength of the neutron moving at 1% of the speed of light is approximately \(1.319 \times 10^{-13} m\).
04

Part b: Calculate the velocity of a neutron with a given wavelength

In this part, we are given the wavelength and need to find the velocity. We can rearrange the de Broglie wavelength formula to calculate the velocity: \(v = \dfrac{h}{m位}\) We are given the wavelength as \(75 pm\), which is equal to \(75\times10^{-12} m\).
05

Calculate the velocity of the neutron

Now, we can plug in the values to calculate the velocity of the neutron: \(v = \dfrac{6.626 \times 10^{-34} Js}{(1.675\times10^{-27} kg)(75\times10^{-12}m)}\) \(v = \dfrac{6.626 \times 10^{-34}}{1.256\times10^{-38}}\) \(v = 5.281\times10^4 m/s\) Therefore, the velocity of a neutron with a wavelength of \(75 pm\) is approximately \(5.281\times10^4 m/s\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write the expected ground-state electron configuration for each of the following. a. the lightest halogen atom b. the alkali metal with only \(2 p\) and \(3 p\) electrons c. the Group \(3 \mathrm{~A}\) element in the same period as \(\mathrm{Sn}\) d. the nonmetallic elements in Group \(4 \mathrm{~A}\)

As the weapons officer aboard the Starship Chemistry, it is your duty to configure a photon torpedo to remove an electron from the outer hull of an enemy vessel. You know that the work function (the binding energy of the electron) of the hull of the enemy ship is \(7.52 \times 10^{-19} \mathrm{~J}\). a. What wavelength does your photon torpedo need to be to eject an electron? b. You find an extra photon torpedo with a wavelength of 259 \(\mathrm{nm}\) and fire it at the enemy vessel. Does this photon torpedo do any damage to the ship (does it eject an electron)? c. If the hull of the enemy vessel is made of the element with an electron configuration of \([\mathrm{Ar}] 4 s^{1} 3 d^{10}\), what metal is this?

The electron affinities of the elements from aluminum to chlorine are \(-44,-120,-74,-200.4\), and \(-384.7 \mathrm{~kJ} / \mathrm{mol}\), respectively. Rationalize the trend in these values.

Order the atoms in each of the following sets from the least exothermic electron affinity to the most. a. \(\mathrm{N}, \mathrm{O}, \mathrm{F}\) b. \(\mathrm{Al}, \mathrm{Si}, \mathrm{P}\)

Give the name and formula of each of the binary compounds formed from the following elements. a. \(\mathrm{Li}\) and \(\mathrm{N}\) b. \(\mathrm{Na}\) and \(\mathrm{Br}\) c. \(\mathrm{K}\) and \(\mathrm{S}\)
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Physical Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.