ATOMIC STRUCTURE.docx

1. PHYSICS
Atomic Structure
ANSWERS
A1 CONCEPT:
 Photoelectric effect: When electromagnetic radiation hits a material, electrons are emitted, this
effect is known as the Photoelectric effect.
o Electrons emitted in this manner are called photo-electrons.
Max Kinetic energy of these photo-electrons are given by:
K.E.max = h f - ϕ
where h is the Planck constant f is the frequency of the incident light or electromagnetic radiation. The
term ϕ is the work function.
 The work function is the property of the material.
EXPLANATION:
 The maximum kinetic energy of the photo-electron is given by
K.E.max = h f - ϕ
where h is the Planck constant f is the frequency of the incident light or electromagnetic radiation. The
term ϕ is the work function.
 From this formula, max K.E. depends on
1. the frequency of the incident electromagnetic radiation (or light).
2. Work function ϕ
 So the correct answer will be option 2.
A2 CONCEPT:
 Photoelectric effect: It is the phenomenon of emission of electrons from the surface of
metals, when light radiations (Electromagnetic radiations) of suitable frequency fall on them.
 The emitted electrons are called photoelectrons and the current so produced is
called photoelectric current.

2. EXPLANATION:
 The minimum energy needed to remove electrons from the metal surface is called work
function (φ) of that metal. Thus option 3 is correct.
 The value of retarding potential at which the photoelectric current is zero is called cut off or
stopping potential for the given frequency of all incident radiation. Thus option 1 is incorrect.
 The maximum energy of ejected electrons from the metal surface after ejection is called
as maximum kinetic energy (KEmax). Thus option 2 is incorrect.
A3 CONCEPT:
 Photoelectric effect: When the light of sufficiently small wavelength is incident on the metal
surface, electrons are ejected from the metal instantly. This phenomenon is called
the photoelectric effect.
 Stopping potential: The photocurrent may be stopped by applying a negative potential to
anode w.r.t. cathode. The minimum potential required to stop the electron emitted from
metal so that its kinetic energy becomes zero is called stopping potential or retarding
potential.
 Intensity: The number of photons falling per unit area is called intensity of the incident light.
EXPLANATION:
 ''The number of photo-electrons emitted per unit area per unit time is directly proportional
to the intensity of incident light.'' So option 1 is correct.
A4 CONCEPT:
 When atoms are excited they emit light of certain wavelengths that correspond to
different colors. Due to the electron making transitions between two energy levels in an atom.
 The light emission can be seen as a series of colored lines, known as atomic spectra.
 These atomic spectra are divided into a number of spectral series. The wavelength related to
these series is given by the Rydberg formula.
 The energy differences between levels in the Bohr model is given by the Rydberg formula. Hence
the wavelengths of emitted/absorbed photons

 Where Z is the atomic number, n1 is the lower energy level orbit, n2 is the upper energy level
orbit, and R∞ is the Rydberg constant (1.09677×107 m−1 for hydrogen and 1.09737×107 m−1 for
heavy metals).
In the Bohr model, spectrum series are given below:

3.  The Lyman series: It includes the lines emitted by transitions of the electron from an outer orbit
of quantum number n2 > 1 to the 1st orbit of quantum number n1 = 1.
o All the energy wavelengths in the Lyman series lie in the ultraviolet band.
 The Balmer series: It includes the lines due to transitions from an outer orbit n2 > 2 to the orbit
n1 = 2.
o Four of the Balmer lines lie in the "visible" part of the spectrum.
 Paschen series (Bohr series, n1 = 3)
 Brackett series (n1 = 4)
 Pfund series (n1 = 5)
EXPLANATION:
 When an electron in Hydrogen atom transit from higher energy orbit to 2nd orbit. (outer
orbit n2 > 2 to the orbit n1 = 2) known as Balmer Series.
 The energy released from this spectrum gives the visible part of the spectrum.
 So the correct answer is option 4.
A5 CONCEPT:
 Rutherford’s Model of the Atom:
 He bombarded the beam of alpha particles on a very thin gold foil.
 While bombarding he observes the number of scattering of particles –
 Most of the particles passed either un-deviated or with very small deviation.
 Some deviated by large angles
 1 out of 8000 was deflected by more than 90°
 Conclusion to this deflection:
 Most of the space of an atom is empty.
 At the center of an atom having a tiny positively charged particle called
a nucleus.
 The center nucleus has all the mass of an atom.
 The amount of positive charge at the nucleus is equal to the total amount of
negative charges on all the electrons of the atom.
 All the electrons revolve around the nucleus and coulomb force provide
centripetal force
EXPLANATION:
This the nucleus of the atom is discovered by Rutherford atomic model. So option 3 is correct.
 Limitations of Rutherford’s Model of the Atom:
 As Rutherford’s Model suggests electrons always revolve around the nucleus.
 From the point of mechanics it is okay as Coulomb force provides the necessary
centripetal force.

4.  But Maxwell’s equation of electromagnetism show any accelerated electron must
continuously emit electromagnetic radiation.
 This revolving electron continuously emit radiation at all temperature.
 This energy spend ultimately makes an electron to fall on the nucleus.
 But in real case hydrogen is very stable nor emit any energy.
A6 CONCEPT:
 The spectral lines of the Lyman series fall in the U.V region for the Hydrogen atom.
 We can predict this using this equation
Where RH = Rydberg constant
 When excited electrons fall from higher energy level to lower energy level, they emit
electromagnetic radiations of discrete frequencies and the emission spectrum is formed.
 Lyman series – when an electron from higher energy level falls to 1st energy level – UV
region.
 Balmer series – when an electron from higher energy level falls to 2nd energy level – Visible
region.
 Paschen series – when an electron from higher energy level falls to the 3rd energy
level – Infrared region.
 Brackett series – when an electron from higher energy level falls to 4th energy level – Infrared
region.
 Pfund series – when an electron from higher energy level falls to the 5th energy level – Infrared
region.
EXPLANATION:
 In a hydrogen atom, the transition of electrons between different energy levels gives spectral
lines of different wavelengths. These lines fall into a specific series.
 We can predict this using this equation

In the Lyman series, the spectral lines correspond to the transition of an electron from a higher to
lower energy level when the quantum number of the final stationary orbit ( nf ) is 1. and it falls
under the UV region.
A7 CONCEPT:
 X-rays: An electromagnetic wave with wavelengths from 0.01 nm to 10 nm called X-rays.
 X-rays are produced when the high-velocity electrons collide with the metal plates and
gave the energy as the X-Rays and themselves absorbed by the metal plate.

5.  It is used to print X-rays of bones.
 Wilhelm Roentgen is the German professor who first discovered the X-rays. So option 4 is
correct.
A8 CONCEPT:
 As per radioactive decay law, the total number of nuclei of radioactive compounds after
radioactive decay in the sample is given by given equation

 where N is the number of nuclei of radioactive compounds after radioactive decay, N0 is
the number of nuclei of radioactive compounds initially, λ is the decay constant and t is the
time of radioactive decay.
 Half-Life: Half-life is the time required for a radioactive substance to reduce to its half initial
value.
CALCULATION:
 From the definition of half-life, radioactive decay in time T (half-life) will be half of its initial value
N = N0 / 2
so at time t = T, no of nuclei is N = N0 / 2
where N0 is the initial number of nuclei.
From radioactive decay law:
⇒ λ T = loge 2
So the correct answer will be option 3.
A9 The Atomic mass is the sum of protons and neutrons.
 In the nucleus of an atom, there are protons and neutrons.
Number of protons = Atomic number of an element.
Nuclei = neutron + proton
EXPLANATION:

6. Given that: mass number = 23 and atomic number = 11.
Number of protons = Atomic number = 11
IMPORTANT POINTS:
 Sodium is a chemical element with Atomic number 11 and Symbol Na.
 Mass number = Number of protons + Number of neutrons, hence the number of neutrons is 12.
 Isotopes are elements having different numbers of neutrons and the same number of protons.
A10 CONCEPT:
 Isotones are the atoms or nuclei which have an equal number of neutrons.
 Cl-37 and K39 both have the same number of neutrons.
 Isobars are Atoms of a chemical element that have the same atomic mass but a different
atomic number.
 Isotopes are Atoms of a chemical element that have the same atomic number but a different
atomic mass.
EXPLANATION:
 From the given definition of Isotones, The correct answer is option 2.
 Isomers are atoms of the same element with the same mass number and atomic number but
which are in different excited states.
A11 CONCEPT:
Nuclear reactor:
 It is a device in which a nuclear reaction is initiated, maintained, and controlled.
 It works on the principle of controlled chain reaction and provides energy at a constant rate.
EXPLANATION:
 The function of the moderator and coolant in the Canada Deuterium Uranium (CANDU)
reactor is performed by heavy water
 The moderator's function is to slow down the fast-moving secondary neutrons produced
during the fission. T
 The material of the moderator should be light and it should not absorb neutrons.
 Usually, heavy water, graphite, deuterium, and paraffin, etc. can act as moderators.
 The heat released by fission in nuclear reactors must be captured and transferred for use in
electricity generation.
 To this end, reactors use coolants that remove heat from the core where the fuel is
processed and carry it to electrical generators.
 Coolants also serve to maintain manageable pressures within the core.

7. A12 CONCEPT:
 The equation that relates the mass and energy is given by Albert Einstein.
 According to the equation, the mass can be converted into equivalent energy and vice versa.
Einstein's equation is given by:
E = m c2
Where E = Energy, m = mass, c = speed of light.
CALCULATION:
Given that:
m = 8 mg = 8 × 10-6 kg
Speed of light (c) = 3 × 108 m/s
To find equivalent energy (E):
We know that
A13 CONCEPT
Bohr model: In 1913, Niels Bohr gave the Bohr's atom model which retained essential features of
Rutherford's model and at the same time took into account its drawbacks.
 The electrons revolve around the nucleus in circular orbits which is called the stationary
orbit.
 According to the Bohr's atom model, the electrons of an atom revolve around the nucleus only in
those orbits in which the angular momentum of the electron is an integral multiple of h /2π.
 By absorbing energy the electrons are able to jump from lower energy(Ei) level to higher
energy level (Ef) and vice versa.
 The energy of emitted radiation is given by
The energy of electrons in any orbit is given by:
Where n is principal quantum number and Z is the atomic number.

8. CALCULATION:
Given - Ground state energy = -13.6 eV, n =2 (Since first excited state) Z =2
 The energy of the nth excited state can be calculated using the equation
 The Energy of the first excited state will be En=−13.6eV
A14 CONCEPT:
 The minimum energy required to remove an electron from the ground state to outside the
atom is called ionization energy.
 The energy of electrons in any orbit is given by:
CALCULATION:
Given that Helium is in the ground state, so
For Helium Z = 2
 The ionization energy of an electron in the ground state of the helium atom E1 = 24.6 eV.
 The energy required to liberate the second electron from helium.
 The total energy required to remove both the electron = E1 + E2
⇒ E1 + E2 = 54.4 eV + 24.6 eV = 79 eV
So the correct answer is option 2.
Where n = principal quantum number and Z = the atomic number
A15 CONCEPT:
 Every electron revolves around the nucleus in the orbits.
 The nucleus is positively charged and the electrons that revolve around the nucleus are
negatively charged, so they attract each other.
 Bohr was the scientist who gave an explanation of Hydrogen.
 Bohr's model of hydrogen is based on the assumption that electrons travel in specific shells, or
orbits, around the nucleus.
 Bohr's model calculated the energy of an electron revolving on different orbits (n):

9. Where n is the orbit number in which the electron is moving.
EXPLANATION:
Given that:
the electron is in 3rd orbit; n = 3
 The energy of an electron at nth orbit is given by
So, the energy of an electron at 3rd orbit will be
So the correct answer is option 1.
A16 CONCEPT:
 Quark: A quark is a fundamental particle of matter. It is a type of elementary particle of atoms.
 There are 6 types of quark (up, down, strange, charm, bottom, and top)
 Quarks combine to form composite particles called hadrons, the most stable hadrons
are protons and neutrons.
o The proton is to be composed of two up quarks, one down quark.
o The neutron is to be composed of two down quarks and one up quark.
o Similarly, the positron is composed of quarks particles.
o π-meson: Any of three subatomic particles: π⁰, π⁺ , and π⁻ are pi meson.
o Pi mesons are the lightest mesons.
EXPLANATION:
 Protons, neutrons, and other hadrons are composed of quarks particles.
 Electron and π-meson are not composed of quarks particles. So the correct answer is option
4.
A17 ONCEPT:
 Rutherford’s Model of the Atom: He bombarded the beam of alpha particles on a very thin
gold foil.
While bombarding he observes the number of scattering of particles:
 Most of the particles passed either un-deviated or with a very small deviation.
 Some deviated by large angles
 1 out of 8000 was deflected by more than 90°
The conclusion of this deflection:
 Most of the space of an atom is empty.

10.  At the center of an atom having a tiny positively charged particle called a nucleus.
 The center nucleus has all the mass of an atom.
 The amount of positive charge at the nucleus is equal to the total amount of negative charges on
all the electrons of the atom.
 All the electrons revolve around the nucleus and coulomb force provides the centripetal force.
EXPLANATION:
 From the above discussion, we can say that very few alpha particles are deviated by 90°. So
option 4 is correct.
A18 CONCEPT:
 Rutherford’s Model of the Atom:
 He bombarded the beam of alpha particles on a very thin gold foil.
 While bombarding he observes the number of scattering of particles –
 Most of the particles passed either un-deviated or with very small deviation.
 Some deviated by large angles
 1 out of 8000 was deflected by more than 90°
EXPLANATION:
 When the alpha particles are bombarded on the gold foil then the nucleus of the god foil repel
the alpha beam and some of the alpha particle reach to a point which is most close to the
nucleus. This distance is called closest distance.
 If the atomic number of the atom is increased then the positive charge on the nucleus will
increases and the force of repulsion on the alpha particles beam will increases.
 Due to the increase in force of repulsion, the closest approach will decrease. Thus it will be
less than that in case of gold foil. So option 1 is correct.
A19 CONCEPT:
 Half-life: The time required for a quantity to reduce to half of its initial value is called the half-
life.
 Mean life: The average lifetime of all the nuclei of a particular unstable atomic species is called
mean life.

11. CALCULATION:
Given that 100 elements emit in 2 sec and 50 elements and next 2 sec,
50 elements are just half of 100 elements. So,
So the correct answer is option 3.
A20 CONCEPT:
 Photoelectric effect: When the light of a suitable wavelength is incident on the metal
surface, electrons are ejected from the metal instantly. This phenomenon is called
the photoelectric effect.
 Stopping potential (V): The minimum potential required to stop the electron emitted from
metal so that its kinetic energy becomes zero is called stopping potential.
 Work function: It is the minimum amount of energy required so that metal emits an
electron. It is represented by ϕ.
 Albert Einstein equation for photoelectric emission:
h ν = ϕ + e V
Where, h = planks constant, ν = incident frequency, ϕ = work function, e = charge on an electron and V
= stopping potential.
CALCULATION:
Given - λ = 200 nm = 2000 A, ϕ0 = 5.01 ev
 Albert Einstein equation for photoelectric emission:
h ν = ϕ + e Vo

12. A21 CONCEPT:
 Stopping potential: The voltage difference required to stop electrons from moving between
plates and creating a current in the photoelectric experiment is called stopping potential.
 In the photoelectric experiment, light is directed onto a metal plate and if the frequency of light
is high enough, electrons are ejected from the surface.
 The stopping voltage is used to determine the kinetic energy that the electrons have as they are
ejected from the metal plate.
 The product of the charge on an electron and the stopping voltage gives us the maximum
kinetic energy of that ejected electron.
e × Vs = 1/2 × m × vmax2
CALCULATION:
Given that vmax = 1.8 × 106 m/s
specific charge (e/v) = 1.8 × 1011 C/Kg
e × Vs = 1/2 × m × vmax2
Vs = 9 volt
So the correct answer is option 3.
A22 CONCEPT:
Louis de Broglie in his theory on wave nature of matter proposed that:
All particles could be treated as matter waves with a wavelength λ. And their frequency is given by
the following equation:
where λ is de Broglie wavelength, h is Planck's const, m is mass, v is the velocity.
 When an electron is accelerated its de Broglie wavelength is given by
where V is the potential difference in which electron is accelerated.

13. CALCULATION:
Given that: potential difference V = 100 volt
So the correct answer is option 2.
A23 Concept-
 When the photons fall on a metal surface then some electrons get ejected from the metal
surface. This phenomenon is called photoelectric effect.
 The minimum energy needed to remove electrons from the metal surface is called work
function (φ) of that metal.
 The maximum energy of ejected electrons from the metal surface after ejection is called
as maximum kinetic energy (KEmax).
Einstein’s equation of photoelectric equation:
E = φ + KEmax
Where E is incident energy of photons, φ is work function of metal and KE is maximum kinetic energy of
electrons.
E = h ν
Where h is Planck constant and ν is frequency of incident radiation
Explanation-
According to Einstein’s photoelectric equation:
E = φ + KEmax
E = h ν
E = φ + KEmax = h ν
KEmax = (h ν - φ)
 Thus maximum kinetic energy depends on the frequency (ν) of incident radiation. Hence
option 2 is correct.
 The maximum kinetic energy doesn’t depend upon the intensity of incident radiations and
number of photons. So options 1 and 4 are wrong.
 Since speed of radiation is always constant and equal to speed of light. So maximum kinetic
energy is independent of the speed of the incident radiations. So option 3 is wrong.

14. Important points:
 When we increase the number of photons or intensity of the incident radiations then the
number of electrons ejected will increase but maximum kinetic energy of electrons will not
change.
A24 Concept-
 The atoms have protons and neutrons in the nucleous of the atom and electrons revolve around
the nucleous in the orbits.
 The time taken by electron to complete one revolution in an orbit is called period of revolution.
The velocity of electron in nth orbit is given by:
Radius of electron in nth orbit is given by:
Where c is speed of light, Z is atomic number, a0 is a constant and n is principle quantum number
The time period of electron is given by:
Explanation-
For hydrogen atom: Z = 1
Given that,
In ground state, n = 1
In first excited state, n = 2
Thus T’ = 8 T
A25 CONCEPT:
Spectrum & Hydrogen Spectrum:
 Spectrum is an arrangement of different wavelengths. This arrangement can be either
continuous or non-continuous.
 The wavelength of emitted radiations is given by the equation

15. where R= Rydberg constant, n1 = initial energy level, n2 = final energy level
CALCULATION
The wavelength of emission is given by
Case 1:
 Third excited state means n2 = 4
 Second excited state means n1 = 3

16. Case 2:
Divide equation 1 and 2, we get
A26 CONCEPT:
Bohr's Atomic Model :
 Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in
which a single electron revolves around a stationary nucleus of positive charge Ze (called
hydrogen-like atom).
EXPLANATION:
Given - n2 = 2 and n1 = 1
 According to the Bohr atomic model, the time period of a revolution is given by
Where n = number of orbit, h = plank's constant, m = mass of electron, Z = atomic number and e =
charge on electron
 According to the questions, we have to find the time period of the revolution of an electron of
a hydrogen atom. So, ϵo, h, m, Z, and e are constant.
∴ T α n3
⇒ T2 = 8 T1
A27 CONCEPT:
HALF-LIFE :
 Half-life ( t12t12)is the time taken by radioactive material to become half of its initial
concentration

17.  If N0 is the initial concentration the time required to become
where λ is the decay constant
CALCULATION:
Given - Initial amount of A1 = 40 g, half-life of radioactive materials A1 = 20 sec, Initial amount of (A2) =
160 g and half-life of radioactive materials A2 = 10 sec
 The relationship between the initial number of particles and the final number of particles in
radioactive decay is given by
Where N = amount of substance after t sec, No = initial number of substance and n = number of half-
lives
For A1,
For A2,
The time t = 40 Sec
A28 CONCEPT:
 Beta-decay: When a nucleus is unstable because it has too many or too few neutrons relative to
protons. The nucleus emits a beta particle and energy.

18.  In beta-minus decay, a neutron breaks down to a proton and an electron, and
the electron is emitted from the nucleus.
 A β-decay is always accompanied by an anti-neutrino.
 Strong nuclear force: The force created between nucleons by the exchange of particles called
mesons.
o Due to this force, the particles protons and neutrons will stick to each other.
o This force doesn't depend on the charge as it works on neutrons (which has no
charge) and protons.
 Stellar energy is the energy of a star. It is a combination of
1. the internal energy of a star.
2. the energy radiated by a star.
3. the energy of the stars.
EXPLANATION:
 From the definition of Nuclear force, this force works inside the nucleus on neutrons and
protons.
o And neutrons are chargeless, so it is clear that the Nuclear force is charge
independent.
o So statement (b) is correct.
 Stellar energy is the energy of a star.
o We know that a star gets its energy from the fusion reaction of Hydrogen and
Helium.
o So statement (c) is correct.
 During a Beta-decay from the above definition, it is clear that A β-decay is always accompanied
by an anti-neutrino.
o So statement (a) is wrong.
 Hence the correct answer will be option 4.