Chapter#04: Atomic Physics - Quanta: BS/MSc Physics Books

Team Quanta gladly presents all possible short questions of Modern Physics & Electronics’ Chapter#04: Atomic Physics.

Q.7.1 The hydrogen atom contains only a single electron and yet hydrogen spectrum contains many lines, why is this so?

Answer: When energy is supplied to hydrogen atom, it will be excited and then its single electron will jump from its ground level to some higher energy level. When it de-excites from higher energy state to ground state by several jumps, spectral lines of different wavelengths are emitted. That is why the spectrum of hydrogen contains many lines.

Q.7.2 Name the different types of emission spectrum.

Answer: There are three kinds of spectrum which are:

Continuous spectra e.g. radiation spectrum of black body
Band spectra e.g. molecular spectrum
Line or discrete spectra e.g. atomic spectrum of hydrogen

Q.7.3 How Bohr’s theory is much suitable to describe the line spectrum?

Answer: According to Bohr’s theory, when electron comes from higher level to lower level, definite energy is obtained and it will cause to produce line spectrum. Thus Bohr’s theory is suitable to describe the line spectrum.

Q.7.4 An electron in a certain atom requires energy of 10.2eV to get excited to another energy level. A photon and an electron both of each have kinetic energies 10.5eV are available.

Answer: To excite an electron, we can supply energy by direct collision with accelerated particles or by photons of energy Accelerated particle can transfer energy to the bound electrons in parts or full whereas photons transfer all energy. Hence electron being a particle, of energy 10.5eV should be used.

Q.7.5 Does quantization of angular momentum for hydrogen atom is agreed with de-Broglie hypothesis?

Answer: Yes, quantization of angular momentum for hydrogen atom is agreed with de-Broglie hypothesis.

Q.7.6 In which regions of electromagnetic spectrum does the hydrogen emission spectrum lie?

Answer: The electromagnetic spectrum of hydrogen emission spectrum lies in ultraviolet region, visible region, infrared region and far infrared region.

Q.7.7 Can the electron in the ground state of hydrogen absorb a photon of energy 13.6eV and greater than 13.6eV?

Answer: As ionization energy of the electron in ground state of hydrogen atom is 13.6eV, so the ionization of an atom can take place with photon of energy 13.6eV or greater than 13.6eV.

Q.7.8 How many electronic orbits are there in hydrogen atom?

Answer: There are infinite orbits in hydrogen atom. Only first orbit is occupied by one electron and remaining all orbits are vacant.

Q.7.9 Is energy conserved when an atom emits a photon of light?

Answer: When atom is excited , energy is supplied to electron in the excited state. When electron returns back to its ground state, this supplied energy is emitted in form of light photon. Hence total energy remains constant.

Q.7.10 what are discrete stationary states of an atom?

Answer: Discrete stationary states of an atom are those in which electron go on moving in their own orbits without radiating any energy.

Q.7.11 Discuss drawbacks in Rutherford atomic model.

Answer: According to Rutherford atom model, an electron revolving around the nucleus adopt the spiral path due to continuous emission of energy and finally it will fall into nucleus, but it is not so.

Q.7.12 Explain why a glowing gas gives only certain wavelengths of light and why that gas is capable of absorbing the same wavelengths? Give a reason why it is transparent to other wavelengths?

Answer: A glowing gas gives only certain wavelengths because in elements there are definite energy states. The transitions between these energy states give discrete wavelengths. So when gas atoms are excited, the photons of same wavelengths can be absorbed which have energy exactly equal to energy difference of two states.

Q.7.13 if sodium atom can easily loose one electron, why cannot it just as easily lose two, three or more electrons?

Answer: Sodium has one electron in 3s level which has high energy and hence can be easily removed from atom. The other electrons in states n = 1 or n = 2, which have low energies. Hence it is difficult to remove more than one electron from sodium atom which requires much more energy than is available in chemical reactions at ordinary temperatures.

Q.7.14 A hydrogen atom state is known to have the quantum number I = 3. What are possible values of

Answer: For $I=3,\ \ n\geq4.\ Since\ \left|m_l\right|\ \le l,\ so\ \left|m_l\right|\le3.\ Also\ we\ know\ that\ m_s=\pm\frac{1}{2}$ .

Q.7.15 what are quantum numbers for all hydrogen atoms belonging to sub-shell for n = 4 and l = 3?

Answer: For n=4 and l=3 m1 has values $0,\pm1,\ \pm2,\pm3.$ Hence there are fourteen possible states.

Q.7.16 what are quantum numbers for two electrons of helium atom in its ground state?

Answer: For ground state n =1, I= 0, so quantum numbers of two electrons are listed below:

n	l	m_l	m_s
1	0	0	1/2
1	0	0	-1/2

Q.7.17 For a hydrogen atom, determine the allowed states corresponding to the principal quantum number n = 2 and calculate the energies of these states.

Answer: For n = 2, . There are three 2p states characterized by quantum numbers:

n	l	m_l
2	1	-1
2	1	0
2	1	1

Q.7.18 Two statements are given, which one is true.

The number of values of that are allowed depends only on l and not on n.
The smallest value of n that can go with a give l is l + 1.

Answer: Both statements are true because the number of values of that are allowed depends only on l and not on n and smallest value of n that can go with a given l is l + 1.

Q.7.19 According to Bohr’s model of the hydrogen atom, what is the uncertainty in the radial coordinate of the electron? In what way does the model violate the uncertainty principle?

Answer: According to Bohr’s theory, the electron is moving in a circle, so uncertainty in its radial coordinate is zero. Thus uncertainty in its radial velocity is zero and uncertainty product is zero instead of ћ. Therefore Bohr’s theory violates the uncertainty principle.

Q.7.20 why do lithium, potassium, and sodium exhibit similar chemical properties?

Answer: These elements have similar chemical properties because these elements have similar electronic configurations.

Q.7.21 Suppose the electron in the hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why should a gas of such hypothetical atoms emit a continuous spectrum rather than the observed line spectrum?

Answer: When an electron revolves around an atomic nucleus, it behaves like a charge in a radio antenna and radiate light with frequency equal to its own frequency of oscillation. Thus, the electron in hydrogen atoms emits a continuous spectrum.

Q.7.22 Could the Stern Gerlach experiment be performed with ions rather then neutral atoms? Explain.

Answer: No, Stern Gerlach experiment cannot be performed with ions rather than neutral atoms because it is difficult separate the atoms with different orientations of magnetic moments.

Q.7.23 what is difference between excitation and ionization energies?

Answer: Excitation energy: If energy supplied to an electron is such that the electron is lifted from its ground state to any of higher allowed orbits, the atom will be excited and the energy supplied is called excitation energy. The excitation energy is equal to difference of energies of the electron in two orbits i.e. $E_2-E_1,\ E_3-E_1\ etc.$

Ionization energy: If energy supplied to an electron is such that the electron is lifted from its ground state to an infinite orbit, the atom is said to be ionized and energy supplied is called ionization energy. It has only one value $E_\infty-E_1=-E_1$ .

Q.7.24 In the hydrogen atom, can the quantum number n increase without limit?

Answer: According to Bohr’s theory of hydrogen atom,

$E_n=-\frac{13.6}{n^2}\left(eV\right)$

As $n\rightarrow\infty,\ E_n=0$ i.e. electron remains in bound state, thus quantum number n can increase without limit in the hydrogen atom.

Q.7.25 what is difference between excitation and ionization potentials?

Answer: Excitation potential: The potential required to lift an electron from ground state to some higher state is called excitation potential.

Ionization potential: The potential required to eject an electron from ground state to infinity is called ionization potential.

Q.7.26 A hydrogen atom has maximum value of as 4. What can you say about rest of its quantum numbers?

Answer: If $\ m_l=4$ ,then $l\geq4.$ Since $n\geq l+1$ , so $n>4$ . Also we know that $m_s=\pm\frac{1}{2}$ .

Q.7.27 why the X-rays cannot be produced from lighter atoms?

Answer: X-rays are those emitted photons which higher frequency and that is only possible from heavy atoms, so X-rays cannot be produced from lighter atoms.

Q.7.28 Compare the Bohr’s theory and the Schrodinger treatment of the hydrogen atom, specifically emphasizing on their treatment of total energy and orbital angular momentum of the atom.

Answer: According to Bohr’s theory electron is moving in a flat circle governed by equation of classical mechanics F = ma whereas Schrodinger’s theory pictures the electron as a cloud of probability amplitude in the three dimensional space around the hydrogen nucleus, with its motion described by a wave equation.

In the Bohr atom model, angular momentum is quantized according to relation,

$L=n\left(\frac{h}{2\pi}\right)$

In the Schrodinger quantum theory, angular momentum is quantized according to relation,

$L=\sqrt{l\left(l+1\right)}\ \hbar$

For hydrogen atom, according to both models the energy of electron has discrete values and given by,

$E_n=-\frac{13.6}{n^2}\left(eV\right);\ \ \ \ n=1,\ 2,\ 3,\ldots$

Q.7.29 why the inner shell transition is basic requirement for production of X-rays?

Answer: Inner shell transition is basic requirement for production of X-rays because transition of inner shell electrons in heavy atoms gives rise to the emission of high energy photons are called x-rays.

Q.7.30 How can we become able to produce highly accelerated X-rays beam by using high potential alternating source?

Answer: We produce highly accelerated X-ray beam by using high potential between cathode and target as a result fast moving electrons from inner most shells such as K or L will be knocked out. When these shells are occupied by transitions of electrons from higher states then high energy X-rays are produced.

Q.7.31 what do you mean by bremsstrahlung?

Answer: Bremsstrahlung is German word meaning to stop or break. Thus bremsstrahlung is that in which continuous spectrum is obtained due to breaking radiation i.e. by deceleration of impacting electrons.

Q.7.32 Name reverse process of X-ray production. What is inner shell transition?

Answer: The reverse process of X-ray production is photo electric effect.

In heavy atoms electrons are assumed to be arranged in concentric shells K, L, N etc. the inner shell electrons are tightly bound to nucleus and large amount of energy is needed for their excitation. When these electrons go back to their parent levels, they emit photons of very high energy. Transitions from these inner shells in heavy atoms are known as inner shell transitions.

Q.7.33 why is stimulated emission so important in the operation of a laser?

Answer: Stimulated emission is important because it coerces atoms to emit photons along a specific axis and in phase rather than in the random directions and phases of spontaneously emitted photons. The fraction allowed to escape constitutes the intense, collimated, and coherent laser beam whereas in spontaneous emission; the emitted photons would not exit the tube or crystal in the same direction.

Q.7.34 why is a non-uniform magnetic field used in the Stern-Gerlach experiment?

Answer: The deflecting (magnetic) force on an atom is proportional to the gradient of the magnetic filed. Thus, atom with oppositely directed magnetic moments would be deflected I opposite directions in n inhomogeneous magnetic field.

Review Questions

R.7.1 The total energy of hydrogen orbits is negative. Why?

Answer: The negative sign shows that electron is bound to the nucleus by electrostatic force of attraction and that energy must be supplied to detach an electron from nucleus.

R.7.2 Can we see all spectral lines of various series of hydrogen atom?

Answer: No, we can see only members of Balmer series while other series are invisible.

R.7.3 If electrons revolving around nucleus come to rest what will happen?

Answer: If electrons revolving around nucleus come to rest, then due to electrostatic attraction electrons will fall into nucleus.

R.7.4 what is Bohr quantization rule? Give limitations of Bohr atomic model.

Answer: Bohr quantization rule is,

$mvr=n\left(\frac{h}{2\pi}\right)$

Limitations of Bohr atomic model are:

Bohr did not tell us why only circular orbits are possible.

He failed to explain spectrum of higher atoms.

R.7.5 How the maximum energy of X-rays emitted from X-ray tube is increased?

Answer: The energy of electrons hitting the target can be increased by increasing potential difference between anode and cathode and hence the frequency of emitted photon increases.

R.7.6 why hydrogen atom cannot emit X-rays?

Answer: Hydrogen atom has only one electron in its K-shell. If this electron in knocked out, there is a vacancy in K-shell but no other electron is available in the higher shell to fill this vacancy. Therefore hydrogen atom cannot emit X-rays.

R.7.7 Differentiate between characteristics X-rays and continuous X-rays.

Answer: The X-rays emitted from inner shell transitions are called characteristics X-rays and their energy depends upon time of target material.

The X-rays emitted having continuous range of frequencies due to bremsstrahlung effect are called continuous X-rays.

R.7.8 Can the frequency of possible discrete lines in the spectrum of hydrogen increase without limit?

Answer: No, for a spectral line, the electron makes a transition from a higher energy level to a lower energy level. The greatest frequency is that of the Lyman series limit, caused by the transition from $n=\infty\ to\ n=1.$ No, for a spectral line, the electron makes a transition from a higher energy level to a lower energy level. the greatest frequency is that of the Lyman series limit, caused by the transition from $n=\infty\ to\ n=1.$

R.7.9 why are three quantum numbers needed to discrete the state a one-electron atom (ignoring spin)?

Answer: Three quantum numbers are needed to describe an orbital wave function because we are concerned with three dimensional space. They arise from boundary condition on the wave function and can be expressed as a product of function of $r,\ \theta,\ \varphi$ .

R.7.10 An energy of about 21eV is required to excite an electron in a helium atom from the 1s state to the 2s state. Explain why the same transition for the ${\rm He}^+$ ion requires twice energy approximately.

Answer: In a neutral helium atom, one electron can be considered as moving in an electric field created by the nucleus and second electron. If the electron is in higher level than ground state it moves in the electric field of charge 2e – e = e. we say the nuclear charge is screened by the inner electron. The electron in an ion moves in the field of the unscreened nuclear charge of 2 protons. Then the potential energy function for the electron is about double that of one electron in the neutral atom.

R.7.11 Does the intensity of light from a laser fall off as $\frac{1}{r^2}$ ? Explain.

Answer: No, the intensity of a laser beam stays almost constant, independent of the distance it has traveled.

R.7.12 (a) Can a hydrogen atom in the ground state absorb a photon of energy less than 13.6eV?

(b) Can this atom absorb a photon of energy greater than 13.6eV?

Answer: (a)-A hydrogen atom in the ground state can absorb a photon of energy less than 13.6eV if the energy of the photon is precisely enough to put the electron into one of the allowed energy states because if the energy of the photon is not sufficient to put the electron into a particular excited energy level, the photon will not interact with the atom.

(b)-A photon of any energy greater than 13.6eV will ionize the atom. Any energy above 13.6eV will go into kinetic energy of the newly liberated electron.

Modern Physics & Electronics