Atomic Structure and Bohr's Model Quiz

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Questions and Answers

What is the relationship between the electrostatic force and the centripetal force acting on an electron orbiting the nucleus, according to Bohr's postulates?

They are equal and opposite forces. (correct)

They are independent of each other.

They are directly proportional to each other.

They are inversely proportional to each other.

According to Bohr's second postulate, what is the allowed value for the angular momentum of an electron in a stationary orbit?

Only values that are half-integral multiples of h/2π.

Only values that are multiples of hc/λ.

Only values that are integral multiples of h/2π. (correct)

Any value that is a multiple of Planck's constant.

Which of the following correctly represents the relationship between the energy difference (ΔE) between two energy levels, the speed of light (c), Planck's constant (h), and the wavelength (λ) of the emitted photon?

ΔE = λ/hc

ΔE = hcλ

ΔE = hλ/c

ΔE = hc/λ (correct)

What is the expression for the velocity of an electron in the nth orbit of a hydrogen atom, according to Bohr's model?

v = (Ze^2 / 4πεοmr) (A) Signup and view all the answers

What is the expression for the radius of the nth orbit of an electron in a hydrogen atom, according to Bohr's model?

r = (n^2h^2 / 4π^2mZe^2) (D) Signup and view all the answers

What does the Gold Foil Experiment demonstrate about the structure of an atom?

Atoms consist of a small, dense nucleus surrounded by a cloud of electrons. (C) Signup and view all the answers

According to Rutherford's atomic model, what provides the centripetal force for the electrons to revolve around the nucleus?

The electrostatic force of attraction between the positively charged nucleus and negatively charged electrons. (B) Signup and view all the answers

What is the primary drawback of Rutherford's atomic model?

It cannot explain the stability of the atom, as electrons should lose energy and spiral into the nucleus. (D) Signup and view all the answers

Which of the following is NOT a characteristic of the Bohr model?

Electrons continuously lose energy in the form of electromagnetic radiation when revolving around the nucleus. (A) Signup and view all the answers

What type of spectrum is observed when an electron in an atom transitions from a higher energy level to a lower energy level?

Emission spectrum (B) Signup and view all the answers

Why are atoms like `He+`, `Li^2+`, and `Na^3+` considered 'H-like' atoms?

They have only one electron orbiting the nucleus, similar to hydrogen. (C) Signup and view all the answers

According to Maxwell's theory, what happens to a charged particle when it accelerates?

It interacts with both electric and magnetic fields, and emits energy. (C) Signup and view all the answers

Based on the information provided, which of the following statements about the Geiger and Marsden Experiment is TRUE?

Most of the alpha particles passed through the gold foil undeflected. (C), Alpha particles were deflected at a wide range of angles, including large angles. (D) Signup and view all the answers

What is the significance of de Broglie's proof in relation to Bohr's second postulate?

It provides a formula for calculating the wavelength of an electron. (A), It defines the relationship between total length of a wave and the circumference of an orbit. (C) Signup and view all the answers

How can the atomic number (Z) of an atom be defined?

The number of protons within the nucleus. (A) Signup and view all the answers

Which equation correctly expresses the relationship between atomic mass number (A) and number of neutrons (N)?

N = A - Z (D) Signup and view all the answers

What limitation did Bohr encounter in explaining atomic phenomena?

He failed to explain the elliptical nature of orbits. (B), He did not consider the effects of magnetic fields. (C) Signup and view all the answers

Calculate the wavelength for the Balmer series given the formula used.

3646.4 Å (C) Signup and view all the answers

How is the total mass of an atom represented?

M = actual mass of an atom (D) Signup and view all the answers

From the equation $n\lambda = 2\pi r$, what does the variable n represent?

Principal quantum number (C), Number of waves in a circular path (D) Signup and view all the answers

What does it mean if a nucleus has an atomic number Z of 92 and atomic mass A of 236?

The total number of nucleons is 236. (B) Signup and view all the answers

What is the process called when light unstable nuclei combine to form stable nuclei?

Nuclear Fusion (D) Signup and view all the answers

Which equation correctly represents the nuclear energy released during a fission event?

Nuclear Energy = [mreact - Mprode]c^2 (B) Signup and view all the answers

What does the decay constant (λ) signify in the law of radioactivity?

The probability of decay per unit time (C) Signup and view all the answers

What is the relationship between the half-life of a radioactive sample and the decay constant?

Half-life is inversely proportional to the decay constant (C) Signup and view all the answers

Which of the following correctly describes the concept of mean life (τ)?

The average lifetime of unstable nuclei before decay (B) Signup and view all the answers

If the initial quantity of a radioactive sample is represented as N0, what does N equal after one half-life?

N0/2 (D) Signup and view all the answers

What is the definition of activity (A) in the context of radioactivity?

The rate of disintegration of a sample (A) Signup and view all the answers

For the reaction `^3Li + p -> 2α`, what is the total mass before the reaction compared to the total mass after the reaction?

Mass before is greater than mass after (D) Signup and view all the answers

Which decay process produces an alpha particle along with a new element?

α-decay (C) Signup and view all the answers

What is the meaning of the term 'λ' in the equation A = λN?

The decay constant (A) Signup and view all the answers

If the half-life (t1/2) of a radioactive substance is 28 years, how many seconds does it represent?

8.835 x 10^9 seconds (C) Signup and view all the answers

What does A represent in the context of radioactive decay?

The number of disintegrations per second (C) Signup and view all the answers

In β-decay, what sequence of particles is produced during the process?

Proton, electron, and anti-neutrino (D) Signup and view all the answers

Which statement about the conservation of charge in nuclear decay is true during β+ decay?

Charge is conserved by emitting a positron (B) Signup and view all the answers

What type of decay involves no change in the atomic number of the nucleus?

γ-decay (C) Signup and view all the answers

What is the relationship between the activity A and the number of atoms N given constant decay constant λ?

A is directly proportional to N (A) Signup and view all the answers

What is the formula for the radius of an electron's orbit in a hydrogen atom according to Bohr's model?

r = 0.53 * (εoh^2n^2 / πme^2 (Z)) (B) Signup and view all the answers

Which equation represents the kinetic energy of an electron in the hydrogen atom according to Bohr's model?

KE = me^4Z^2 / 8εoh^2n^2 (D) Signup and view all the answers

What does the equation ΔE = hc / λ calculate in the context of atomic transitions?

The wavelength of emitted or absorbed radiation (C) Signup and view all the answers

Which formula describes the energy of the hydrogen atom at a specific energy level n?

E = -me^4Z^2 / 8εoh^2n^2 (D) Signup and view all the answers

According to Bohr's model, how is the frequency (f) of an electron's orbit calculated?

f = 1/T (A) Signup and view all the answers

What is the relationship of the Rydberg constant (R) to the wavelength of light emitted by an electron transition?

R = 1.097 * 10^7 Z^2 m^-1 (C) Signup and view all the answers

Which series of transitions in the hydrogen energy spectrum falls within the visible range?

Balmer series (B) Signup and view all the answers

What drawback exists in Bohr's atomic model regarding the spectral lines?

It does not account for fine-line spectra. (B) Signup and view all the answers

Study Notes

Atomic and Nuclear Physics

Geiger-Marsden Experiment (Gold Foil Experiment): Alpha particles were directed at a thin gold foil. Most passed straight through, but some were deflected at large angles. This indicated the atom's structure contained a small, dense, positively charged nucleus.
Rutherford Atomic Model: The atom consists mostly of empty space, with a concentrated, positively charged nucleus at the center. Electrons orbit the nucleus.
Drawbacks of Rutherford Model: The model couldn't explain why electrons don't spiral into the nucleus. Classical physics predicts electrons should lose energy and fall into the nucleus.

Bohr Atomic Model

Bohr's First Postulate: Electrons orbit the nucleus in circular paths (orbits). The centripetal force is provided by the electrostatic attraction between the nucleus and the electron.
- The equation to model this is: $mv^2/r = kZe^2/r^2$
Bohr's Second Postulate: Electrons can only exist in specific quantized energy states, or orbits. Angular momentum is quantized: $L = n\hbar$, where n is a positive integer (n=1, 2, 3...).
Bohr's Third Postulate: When an electron jumps from a higher energy orbit to a lower energy orbit, a photon is emitted with energy equal to the difference in energy levels.
- The equation to model this is ΔE = E_f - E_i= hc/λ

Atomic Spectra

Atomic Spectra (from Bohr's Third Postulate): Atoms emit light only at specific wavelengths, producing discrete spectra.

Hydrogen Energy Spectrum

Hydrogen Energy Levels: Electron energy levels are quantized and negatively, described by the equation: $E_n = -13.6 eV/n^2$ with increasing n, the energy increases.
Spectral Series (Lyman, Balmer, Paschen...): Electrons transitioning between different energy levels result in different series of spectral lines (Lyman, Balmer, Paschen) observable in the ultraviolet, visible, and infrared regions.

Nucleus

Nucleons: Particles present inside the nucleus (protons and neutrons).
Atomic Number (Z): The number of protons present inside the nucleus – also the number of electrons in a neutral atom.
Atomic Mass Number (A): Total number of nucleons (protons + neutrons).
Atomic Mass (M): Actual mass of an atom.
Neutrons (N): A = Z + N – The difference between the atomic mass and the atomic number.
Nuclear Notation: ${}_Z^AX$ – A representation of an atom where A is the atomic mass number and Z is the atomic number
Mass of subatomic Particles: Mass of protons is 1.00727 amu, neutrons 1.00866 amu, electrons 0.00055 amu (where amu= atomic mass units)

Nuclear Forces

Nuclear Force: A strong attractive force to bind nucleons inside the nucleus. It is stronger than electromagnetic force but only acts over short distances (10^-15 m).
Nuclear Force Characteristics: Attractive in nature, charge independent and short range

Mass Defect and Binding Energy

Mass Defect (Δm): The difference in mass between the sum of the masses of the individual protons and neutrons in a nucleus, and the actual mass of the nucleus. (e.g (Z_mp + (A-Z)_mn) – M)
Binding Energy (BE): Amount of energy required to separate a nucleus into its constituents, equal to the mass defect multiplied by the speed of light squared (BE = Δm c²).
Binding Energy per Nucleon: The binding energy divided by the number of nucleons (A). High BE/nucleon indicates increased nuclear stability.

Nuclear Reactions

Nuclear Fusion: Combining light nuclei to form a heavier, more stable nucleus. (e.g. Deuterium nuclei fusing to form Helium).
Nuclear Fission: Splitting a heavy nucleus into lighter ones.

Radioactive Decay

Radioactivity: The process of disintegration of unstable nuclei to form stable daughter nuclei.
- The rate of disintegration is proportional to the number of radioactive nuclei. This rate gives rise to the concepts of Half life, t_1/2, and Mean life, τ.
Half-life (t_1/2): The time required for half of the radioactive nuclei to decay.
- t_1/2 = 0.693/λ
Mean life (τ): Average time for a radioactive nucleus to decay
- τ = 1/λ
Activity (A): The rate of disintegration of a sample—measured in dps (disintegrations per second) or Bq (Becquerel).
Different Types od Radioactive Decay: Alpha decay (α), beta decay (β−, β+), gamma decay (γ), positron emission, electron capture etc

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Description

Test your knowledge on atomic structure based on Bohr's model and related concepts. This quiz covers key topics such as electrostatic and centripetal forces, angular momentum, and the implications of the Gold Foil Experiment. Perfect for students studying atomic theory and foundational physics.