Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

(a) What is the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines? (b) What is the wavelength of the series limit?

(a) The wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines is 658 nm.

(b) Thus, the wavelength of the series limit is 366 nm.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identification of the given data

The given data is listed below as-

The photon emitted in the Balmer series is the least energetic.

Step 2: The energy equation is given by

The energy difference is given by the equation-

$∆ E = (13.6 e V) (\frac{1}{n_{2}^{2}} - \frac{1}{n_{1}^{2}})$

Here, n is the quantum number.

Step 3: To determine the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines (a)

The difference between energies is given by the equation:

$∆ E = E_{3} - E_{2} ∆ E = - (13.6 e V) (\frac{1}{n_{2}^{2}} - \frac{1}{n_{1}^{2}})$

For, $n^{2} = 3$ and $n_{1} = 2$

$∆ E = - (13.6 e V) (\frac{1}{3^{2}} - \frac{1}{2^{2}}) = 1.889 e V$

Now, hc = 1240 eV.nm

$λ = \frac{h c}{∆ E} = \frac{1240 e V . n m}{1.889 e V} = 658 n m$

Thus, the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines is 658 nm.

Step 4: To determine the wavelength of the series limit. (b)

The difference between energies is given by the equation:

$∆ E = E_{\infty} - E_{2} ∆ E = - (13.6 e V) (\frac{1}{n_{2}^{2}} - \frac{1}{n_{1}^{2}})$

For, $n_{2} = \infty$ and $n_{1} = 2$

$∆ E = - (13.6 e V) (\frac{1}{\infty^{2}} - \frac{1}{2^{2}}) = 3.40 e V$

Now, hc = 1240 eV.nm

$λ = \frac{h c}{∆ E} = \frac{1240 e V . n m}{3.40 e V} = 366 n m$

Thus, the wavelength of the series limit is 366 nm.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

(a) What is the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines? (b) What is the wavelength of the series limit?

Step by Step Solution

Step 1: Identification of the given data

Step 2: The energy equation is given by

Step 3: To determine the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines (a)

Step 4: To determine the wavelength of the series limit. (b)

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

(a) What is the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines? (b) What is the wavelength of the series limit?

Step by Step Solution

Step 1: Identification of the given data

Step 2: The energy equation is given by

Step 3: To determine the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines (a)

Step 4: To determine the wavelength of the series limit. (b)

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics