# Fundamentals of Physics Chapter 39 Solutions: More About Matter Waves

Resnick Halliday & Walker Fundamentals of Physics Volume 2 Solutions for Chapter 39 ‘More About Matter Waves’ is a perfect guide for those aiming to clear competitive exams like JEE and NEET. In this chapter of Resnick Halliday Physics solutions, you will learn about string waves and matter waves, energies of a trapped electron, wave functions of a trapped electron, an electron in a finite and infinite potential well, 2D and 3D electron traps, Bohr’s Model of hydrogen, Schrodinger Equation and the Hydrogen atom.

Resnick Halliday & Walker Physics Volume 2 More About Matter Waves includes more than 100 practice questions based on higher-order thinking. These questions are divided into 7 different modules related to Energies of a Trapped Electron, Wave Function of a Trapped electron, Electron in a Finite Well, 2D and 3D electron traps, and The Hydrogen Atom. We have provided step by step solutions to each exercise module of this chapter for your assistance. These solutions for Resnick Halliday & Walker More about Matter Waves will help you form a solid foundation for Class 12 board exams as well.

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## Important Topics for Resnick Halliday & Walker Fundamentals of Physics Volume 2 Solutions Chapter 39: More about Matter Waves

The key ideas presented in Chapter 39 of Resnick Halliday and Walker Fundamentals of Physics Volume 2 will teach you how to calculate the energy levels of various quantum levels, angular momentum and wavelength of light.

**String Waves and Matter Waves**– waves can be of two kinds. If a stretched string is of infinite length, we can set up travelling waves of essentially any frequency. However, if a stretched string has only a finite length and is rigidly clamped at both ends, we can set up only standing waves. Such waves are known as string waves.

Matter waves are described as hypothetical waves that are associated with the motion of an atomic or subatomic sized particle which shows effects such as diffraction of beams of particles (for example electrons).

**Confinement principle –**This principle states that ‘Confinement of a wave leads to quantization—that is, to the existence of discrete states with discrete energies’.**De-****Broglie’s hypothesis**– this hypothesis states that all matter exhibits wave-like properties and proposes to establish a relationship between the observed wavelength of matter to its momentum.

de Broglie proposed the relationship as

λ= h / p = h / √(2mE) [ p= Planck’s constant]

This wavelength is said to be de Broglie’s wavelength.

**Correspondence principle – It states that the behaviour of systems described by the old quantum theory reproduces classical physics in the limit of large quantum numbers.**

- Zero-point energy – According to quantum physics, confined systems cannot exist in states with zero energy and must always have certain minimum energy called the zero-point energy.

- Normalizing the wave function – Normalization of a wave function ψ(x,t) is the probability density for finding the particle at point x, at time t. Since the particle must be found somewhere between x=-∞ and x=+∞ the wave function must obey the normalization condition.

- Nanocrystallites – a semiconducting material in powder form having granules in the nanometer range and uniform size each of which can act as a potential well for an electron trapped within it.

### Discussion of Exercises of Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions Chapter 21: Coulomb’s Law

**Questions**

The first set of exercises has 15 questions based on the energies of the trapped electron and the hydrogen atom.

**Module 1: Energies of a Trapped electron **

Module 1 has 12 questions and is based on the Energy formula of electrons. Here you will find problems related to concepts of the ground state and 1D electron traps. You will have to apply the formula for electrons trapped in an infinite potential well also and the sums are mostly of easy grade.

**Module 2: Wave functions of a trapped electron **

Module 2 has only 4 questions which are based on formulas of energies of trapped electrons. Here also you get to solve problems regarding energies of electrons trapped in an infinite potential well but these sums are of second-level on the difficulty scale.

**Module 3: An electron in a finite well**

Module 3 has only 5 questions based on the formula used for electrons trapped in a finite well.

**Module 4: Two- and three- dimensional electron traps**

Module 4 has 9 questions pertaining to energy changes of an electron on changing its energy levels.

**Module 5: The Hydrogen Atom**

Module 5 consists of 25 questions that pertain to formulas used for Hydrogen atom sums.

**Additional Problems**

The last section is the ‘additional problems’ that has a total of 18 questions. It encompasses all the theories discussed in the chapter like string waves and matter waves, energies of a trapped electron, wave functions of a trapped electron, an electron in a finite and infinite potential well, 2D and 3D electron traps, Bohr’s Model of hydrogen, Schrodinger Equation and about the Hydrogen atom.

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