Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 141

Owls have good night vision because their eyes can detect a light intensity as low as \(5.0 \times 10^{-13} \mathrm{~W} / \mathrm{m}^{2}\). Calculate the number of photons per second that an owl's eye can detect if its pupil has a diameter of \(9.0 \mathrm{~mm}\) and the light has a wavelength of \(500 \mathrm{nm}\) \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\)

Short Answer

Expert verified
The result corresponds to the number calculated in the last step. The exact value depends on the constants and values provided, such as the Planck's constant, the speed of light and the values given in the exercise (intensity, diameter and wavelength)

Step by step solution

01

Calculating the area of the owl's pupil

Using the diameter of the owl's eye, calculate the area of the pupil. This is a circular area, so the formula to calculate the area is \(\pi (\frac{d}{2})^2\), where d is the diameter of the circle. The diameter is given as 9 mm, which should be converted to meters (i.e., multiplied by \(10^{-3}\)) to keep the units consistent.
02

Calculating the power of light reaching the owl's eye

Multiply the light intensity (in W/m\(^2\)) which the owl's eye can detect by the area of the pupil. The intensity of light is given as \(5.0 \times 10^{-13}\) W/m\(^2\). This gives the power in watts.
03

Calculating the energy of a single photon

Based on the wavelength of the light, calculate the energy of a single photon. The formula for energy of a photon is \( \frac{hc}{λ}\), where h is the Planck’s constant (\(6.63 \times 10^{-34}\) Js), c is the speed of light (\(3.0 \times 10^8\) m/s), and \(λ\) is the wavelength of light. The wavelength is given in nanometers and should be converted to meters (i.e., multiplied by \(10^{-9}\)).
04

Calculating the number of photons per second

Finally, calculate the number of photons per second. This is done by dividing the power of light reaching the owl's eye by the energy of a single photon. This gives the number of photons per second that an owl's eye can detect.

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

An electron in an atom is in the \(n=3\) quantum level. List the possible values of \(\ell\) and \(m_{\ell}\) that it can have.

Describe the four quantum numbers used to characterize an electron in an atom.

Which orbital in each of the following pairs is lower in energy in a many- electron atom? (a) \(2 s, 2 p ;\) (b) \(3 p, 3 d ;\) (c) \(3 s, 4 s ;\) (d) \(4 d, 5 f\)

Define the following terms and give an example of each: transition metals, lanthanides, actinides.

Indicate the number of unpaired electrons present in each of the following atoms: \(\mathrm{B}, \mathrm{Ne}, \mathrm{P}, \mathrm{Sc}, \mathrm{Mn}, \mathrm{Se}\) \(\mathrm{Kr}, \mathrm{Fe}, \mathrm{Cd}, \mathrm{I}, \mathrm{Pb}\)
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Chemistry Branches

Read Explanation

Organic Chemistry

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