Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 2

Magnetic resonance imaging (MRI) is a powerful diagnostic tool used in medicine. The imagers used in hospitals operate at a frequency of \(4.00 \times 10^{2} \mathrm{MHz}\left(1 \mathrm{MHz}=10^{6} \mathrm{~Hz}\right) .\) Calculate (a) the wavelength. (b) the energy in joules per photon. (c) the energy in kilojoules per mole.

Short Answer

Expert verified
Question: An MRI machine operates at a frequency of \(4.00 \times 10^2 MHz\). Calculate the following: a) The wavelength of the radiation b) The energy in joules per photon c) The energy in kilojoules per mole Answer: a) Wavelength: 7.5 x \(10^{-2}\) m b) Energy per photon: 2.65 x \(10^{-25}\) J c) Energy per mole: 0.1595 kJ/mol

Step by step solution

01

Convert the frequency to Hz

The frequency given is in MHz, so we need to convert it to Hz by multiplying with \(10^6\). This will give us: \(f = 4.00 \times 10^2 MHz \times 10^6 Hz/MHz = 4.00 \times 10^8 Hz\)
02

Calculate the wavelength

Using the speed of light relation \(c = f * \lambda\), we can find the wavelength as follows: \(\lambda = \frac{c}{f} = \frac{3.00 \times 10^8 m/s}{4.00 \times 10^8 Hz} = 0.750 \times 10^{-1} m = 7.5 \times 10^{-2} m\)
03

Calculate the energy per photon

Using the energy per photon formula \(E = h * f\), we can calculate the energy per photon: \(E = (6.626 \times 10^{-34} Js) \times (4.00 \times 10^8 Hz) = 2.65 \times 10^{-25} J\)
04

Calculate the energy per mole

Finally, using the energy per mole formula \(E_{mole} = E * N_A\), we can calculate the energy per mole: \(E_{mole} = (2.65 \times 10^{-25} J) \times (6.022 \times 10^{23} mol^{-1}) = 0.001595 \times 10^2 kJ/mol = 0.1595 kJ/mol\) So, the answers for each part of the question are: a) Wavelength: 7.5 x 10^{-2} m b) Energy per photon: 2.65 x 10^{-25} J c) Energy per mole: 0.1595 kJ/mol

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Give the symbol of the element of lowest atomic number whose ground state has (a) a completed \(\mathrm{f}\) subshell. (b) \(20 \mathrm{p}\) electrons. (c) two \(4 \mathrm{~d}\) electrons. (d) five 5p electrons.

For the following pairs of orbitals, indicate which is higher in energy in a many-electron atom. (a) \(3 \mathrm{~s}\) or \(2 \mathrm{p}\) (b) 4 s or \(4 \mathrm{~d}\) (c) \(4 \mathrm{f}\) or \(6 \mathrm{~s}\) (d) 1 s or \(2 \mathrm{~s}\)

In what main group(s) of the periodic table do element(s) have the following number of filled p orbitals in the outermost principal level? (a) 0 (b) 1 (c) 2 (d) 3

Which of the four atoms \(\mathrm{Na}, \mathrm{P}, \mathrm{Cl}\), or \(\mathrm{K}\) (a) has the largest atomic radius? (b) has the highest ionization energy? (c) is the most electronegative?

A photon of violet light has a wavelength of \(423 \mathrm{~nm} .\) Calculate (a) the frequency. (b) the energy in joules per photon. (c) the energy in kilojoules per mole.
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Physical Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Making Measurements

Read Explanation

The Earths Atmosphere

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.

Sign-up for free