• Home
  • Textbooks
  • Solid State Electronic Devices
  • Atoms and Electrons

Solid State Electronic Devices

Ben G. Streetman, Sanjay Kumar Banerjee

Chapter 2

Atoms and Electrons - all with Video Answers

Educators

Chapter Questions

02:42

Problem 1

(a) Sketch a simple vacuum tube device and the associated circuitry for measuring $E_{m}$ in the photoelectric effect experiment. The electrodes can be placed in a sealed glass envelope.
(b) Sketch the photocurrent $I$ vs. retarding voltage $V$ that you would expect to measure for a given electrode material and configuration. Make the sketch for several intensities of light at a given wavelength.
(c) The work function of platinum is $4.09 \mathrm{eV}$. What retarding potential will be required to reduce the photocurrent to zero in a photoelectric experiment with Pt electrodes if the wavelength of incident light is $2440 \mathrm{~A}$ ? Remember that an energy of $q \Phi$ is lost by each electron in escaping the surface.

Suzanne W.
Suzanne W.
Numerade Educator
03:52

Problem 2

In a photoelectric effect experiment, the threshold wavelength for the ejection of photoelectrons from zinc is $310 \mathrm{~nm} .$ Calculate the work function for Zinc. Also, calculate the velocity for the photoelectrons by light of wavelength 2000 ? other than threshold.

CG
Coleman Green
Numerade Educator
05:28

Problem 3

(a) Show that the various lines in the hydrogen spectrum can be expressed in angstroms as
$$
\lambda(\dot{A})=\frac{911 \mathbf{n}_{1}^{2} \mathbf{n}^{2}}{\mathbf{n}^{2}-\mathbf{n}_{1}^{2}}
$$
where $\mathbf{n}_{1}=1$ for the Lyman series, 2 for the Balmer series, and 3 for the Paschen series. The integer $\mathbf{n}$ is larger than $\mathbf{n}_{1}$.
(b) Calculate $\lambda$ for the Lyman series to $\mathbf{n}=5$, the Balmer series to $\mathbf{n}=7$, and the Paschen series to $\mathbf{n}=10 .$ Plot the results as in Fig. $2-2 .$ What are the wavelength limits for each of the three series?

Robert Schnibbe
Robert Schnibbe
Numerade Educator
01:43

Problem 4

Using Heisenberg's uncertainty principle, estimate the momentum uncertainty of a bound electron within an atom of diameter $10 \mathrm{fm}$. Use this calculated momentum uncertainty to find the minimum binding energy.

Nicholas Mogoi
Nicholas Mogoi
Numerade Educator
03:40

Problem 5

From Balmer's series calculation, first line in the $\mathrm{H}$ spectrum exhibits wavelength of $656.1 \mathrm{~nm}$. Bohr's theory supports almost similar kind of radiative transition by transition of electron of $\mathrm{H}$ atom from third to second energy level. From this, find the value of the Rydberg constant.

Keshav Singh
Keshav Singh
Numerade Educator
04:47

Problem 6

Consider an electron with a normalized wave function defined as $\varphi(x)=2 \alpha \sqrt{\alpha} u e^{-\alpha x}$ for $x>0=0$ for $x<0$
(a) For what value of $x$ does $P(x)=|\varphi(x)|^{2}$ is at peak?
(b) Calculate $\left\langle x>\right.$ and $<x^{2}>$.
(c) What is the probability of finding the particle between $x=0$ and $x=1 / \alpha ?$

Sheh Lit Chang
Sheh Lit Chang
University of Washington
04:36

Problem 7

A particle is described in 1-D by a wavefunction:
$\psi=\mathrm{Be}^{-2 x}$ for $x \geq 0$ and $\mathrm{Ce}^{+4 x}$ for $x<0$, and $\mathrm{B}$ and $\mathrm{C}$ are real constants. Calculate $\mathrm{B}$ and $\mathrm{C}$ to make $\psi$ a valid wavefunction. Where is the particle most likely to be?

Jacob Schulze
Jacob Schulze
Numerade Educator
04:47

Problem 8

The electron wavefunction is $\mathrm{Ce}^{\mathrm{lkx} \text { . between } x}=2$ and $22 \mathrm{~cm}$, and zero everywhere else. What is the value of $\mathrm{C}$ ? What is the probability of finding the electron between $x=0$ and $4 \mathrm{~cm} ?$

Sheh Lit Chang
Sheh Lit Chang
University of Washington
12:45

Problem 9

We define a potential well having energies $V$ as a function of position $x$, as follows:
$V=\infty$ for $x=-0.5 \mathrm{~nm}$ to $0 ; V=0 \mathrm{eV}$ for $x=0$ to $5 \mathrm{~nm} ; V=10 \mathrm{eV}$
for $x=5$ to $6 \mathrm{~nm}$, and $\mathrm{V}=0$ for $x>6 \mathrm{~nm}$ and $x<-0.5 \mathrm{~nm}$. We put an electron with energy $7 \mathrm{eV}$ in the region $x$, between 0 and $5 \mathrm{~nm}$. What is the probability of finding the electron at $x<0 \mathrm{~nm} ?$ Is the probability of finding the electron at $x>6 \mathrm{~nm}$ zero or nonzero? What is this probability for $x>6 \mathrm{~nm}$ if the electron was described by classical mechanics and not quantum mechanics?

Ren Jie Tuieng
Ren Jie Tuieng
Numerade Educator
00:54

Problem 10

Discuss the number of electrons, protons, and neutrons present in the carbon
(C) atom by analyzing its electronic shell structure.

Aadit Sharma
Aadit Sharma
Numerade Educator
01:10

Problem 11

Calculate the first 5 energy levels for an electron trapped in an infinite quantum well (QW) of width $0.59 \mathrm{~nm}$.

Suzanne W.
Suzanne W.
Numerade Educator
04:59

Problem 12

An electron within an atom is described by the following wave function: $\varphi(x, t)=\frac{e^{-i E_{i} t}}{\hbar} \varphi_{1}(x)+\frac{e^{-i E_{J}}}{\hbar} \varphi_{2}(x) .$ Calculate the expectation value of the energy and the energy separation $\Delta \mathrm{E}$.

Ren Jie Tuieng
Ren Jie Tuieng
Numerade Educator
01:33

Problem 13

Schematically show the number of electrons in the various subshells of an atom with the electronic shell structure $1 s^{2} 2 s^{2} 2 p^{4}$ and an atomic weight of $21 .$ Indicate how many protons and neutrons there are in the nucleus. Is this atom chemically reactive, and why?

Shahab Ullah
Shahab Ullah
Numerade Educator