Question 1

Which of the following statements correctly describes the process of photon absorption in a hydrogen atom?

Accepted Answer

Correct Option: B. Solution: Photon absorption occurs when an electron in a lower energy state absorbs a photon with energy equal to the difference between its current energy level and a higher energy level, causing the electron to move to the higher energy level.

Question 2

What is the Bohr radius $a_0$ for the ground state of hydrogen?

Accepted Answer

Correct Option: A. Solution: The Bohr radius $a_0$ for the ground state of hydrogen is $5.3 	imes 10^{-11} 	ext{ m}$.

Question 3

In Bohr's model, what is the relationship between the angular momentum of an electron and Planck's constant?

Accepted Answer

Correct Option: B. Solution: Bohr's second postulate states that the angular momentum of an electron is quantized and is an integral multiple of $h/2\pi$, where $h$ is Planck's constant.

Question 4

In the Geiger-Marsden experiment, what was the primary observation that led to the conclusion of a small, dense atomic nucleus?

Accepted Answer

Correct Option: A. Solution: The observation that most alpha particles passed through the gold foil without deflection indicated that atoms are mostly empty space, leading to the conclusion of a small, dense nucleus.

Question 5

In the context of the Geiger-Marsden experiment, what is the significance of the distance of closest approach for an alpha particle?

Accepted Answer

Correct Option: B. Solution: The distance of closest approach gives an estimate of the upper limit of nuclear size, as it represents the point where an alpha particle's kinetic energy is completely converted into electrostatic potential energy.

Question 6

In the context of atomic spectra, which of the following transitions would result in the emission of a photon?

Accepted Answer

Correct Option: A. Solution: Emission of a photon occurs when an electron transitions from a higher energy level to a lower energy level, releasing energy in the form of a photon.

Question 7

What is the energy required to ionize a hydrogen atom from its ground state?

Accepted Answer

Correct Option: A. Solution: The ionization energy of a hydrogen atom in its ground state is 13.6 eV, as this is the energy required to remove the electron from the atom completely.

Question 8

In the context of the hydrogen atom, what does a negative total energy indicate about the electron's state?

Accepted Answer

Correct Option: B. Solution: A negative total energy for an electron in a hydrogen atom indicates that the electron is bound to the nucleus. It signifies that energy is required to remove the electron from the atom.

Question 9

In the Geiger-Marsden experiment, what was the primary observation that led to the conclusion of a dense nucleus?

Accepted Answer

Correct Option: B. Solution: The observation that a small fraction of alpha particles were deflected at large angles suggested the presence of a dense, positively charged nucleus.

Question 10

If the alpha-particle scattering experiment were conducted with a thin sheet of solid hydrogen instead of gold, what would be the expected outcome?

Accepted Answer

Correct Option: B. Solution: Since hydrogen nuclei are much lighter than gold nuclei, fewer alpha particles would be deflected at large angles due to the reduced nuclear charge and mass.

Question 11

In the context of Rutherford's experiment, if an alpha-particle is observed to scatter at a large angle, what can be inferred about its impact parameter?

Accepted Answer

Correct Option: B. Solution: A large scattering angle suggests a small impact parameter, meaning the alpha-particle approached the nucleus closely, experiencing a strong repulsive force.

Question 12

Consider a hydrogenic atom with a nucleus of charge $+Ze$ and a single electron. According to Bohr's model, what is the expression for the radius of the electron's orbit in the $n^{th}$ energy level?

Accepted Answer

Correct Option: A. Solution: For a hydrogenic atom, the radius of the electron's orbit in the $n^{th}$ energy level is given by $r_n = \frac{n^2 h^2}{4 \pi^2 m e^2 Z}$, where $h$ is Planck's constant, $m$ is the mass of the electron, $e$ is the charge of the electron, and $Z$ is the atomic number.

Question 13

If an electron in a hydrogen atom transitions from the n = 3 state to the n = 2 state, what is the energy of the photon emitted?

Accepted Answer

Correct Option: A. Solution: The energy difference between the n = 3 and n = 2 states is $E_3 - E_2 = -1.51 \, 	ext{eV} - (-3.4 \, 	ext{eV}) = 1.89 \, 	ext{eV}$, which is the energy of the emitted photon.

Question 14

According to Bohr's model, which of the following transitions will result in the emission of a photon with the highest energy?

Accepted Answer

Correct Option: C. Solution: The transition from $n=2$ to $n=1$ involves the largest energy difference, resulting in the emission of a photon with the highest energy.

Question 15

In the context of atomic spectra, what happens when a photon with energy equal to the difference between two energy levels is absorbed by an atom?

Accepted Answer

Correct Option: B. Solution: When a photon with energy equal to the difference between two energy levels is absorbed, the atom transitions to a higher energy state, resulting in an absorption line in the spectrum.

Question 16

In Rutherford's nuclear model of the atom, what is the primary reason most alpha particles pass through the gold foil with little or no deflection?

Accepted Answer

Correct Option: B. Solution: According to Rutherford's model, the atom is mostly empty space, allowing most alpha particles to pass through without deflection. Only when they come close to the dense, positively charged nucleus do they experience significant deflection.

Question 17

Which of the following statements best explains why Bohr's model cannot be extended to multi-electron atoms?

Accepted Answer

Correct Option: A. Solution: Bohr's model is limited to hydrogenic atoms because it does not account for the interactions between electrons, which are significant in multi-electron atoms.

Question 18

Which of the following statements about the alpha-particle scattering experiment is true?

Accepted Answer

Correct Option: B. Solution: The alpha-particle scattering experiment revealed that the atom consists of a dense nucleus, which is responsible for the deflection of alpha-particles at large angles.

Question 19

According to Bohr's second postulate, the angular momentum of an electron in a stable orbit is quantized. Which of the following expressions correctly represents this quantization?

Accepted Answer

Correct Option: A. Solution: Bohr's second postulate states that the angular momentum of an electron in a stable orbit is quantized and given by $L = nh/2\pi$, where $n$ is an integer and $h$ is Planck's constant.

Question 20

In Bohr's model, when an electron transitions from a higher energy orbit to a lower energy orbit, a photon is emitted. What is the relationship between the energy of the photon and the initial and final energy states of the electron?

Accepted Answer

Correct Option: B. Solution: According to Bohr's third postulate, when an electron transitions between orbits, the energy of the emitted photon is equal to the difference in energy between the initial and final states, given by $h
u = E_i - E_f$.

Question 21

According to Rutherford's nuclear model, what is the approximate size of the nucleus compared to the size of the atom?

Accepted Answer

Correct Option: B. Solution: Rutherford's model states that the nucleus is about 10,000 to 100,000 times smaller than the atom, with nuclear size around $10^{-15}$ m to $10^{-14}$ m compared with atomic size around $10^{-10}$ m.

Question 22

Which of the following correctly describes the process that occurs when an atom absorbs a photon?

Accepted Answer

Correct Option: C. Solution: When an atom absorbs a photon, its electron moves to a higher energy state, as the photon provides the exact energy needed for this transition.

Question 23

In the Bohr model of the hydrogen atom, what is the significance of the quantization of angular momentum?

Accepted Answer

Correct Option: B. Solution: The quantization of angular momentum in Bohr's model ensures that electrons can only occupy certain stable orbits, preventing them from spiraling into the nucleus and thus maintaining atomic stability.

Question 24

Which of the following statements best describes the significance of the impact parameter in the Rutherford scattering experiment?

Accepted Answer

Correct Option: C. Solution: The impact parameter is defined as the perpendicular distance from the initial velocity vector of the alpha particle to the center of the nucleus, affecting the scattering angle.

Question 25

What does the Rutherford model fail to explain about the atomic structure?

Accepted Answer

Correct Option: B. Solution: Rutherford's model could not explain the stability of atoms or why atoms emit light of only discrete wavelengths, which are explained by quantum mechanics.

Question 26

In Bohr's model, what happens when an electron transitions from a higher energy state to a lower energy state?

Accepted Answer

Correct Option: C. Solution: According to Bohr's third postulate, when an electron transitions to a lower energy state, a photon is emitted with energy equal to the energy difference between the initial and final states.

Question 27

In the Bohr model of the hydrogen atom, what is the expression for the energy of an electron in the nth orbit?

Accepted Answer

Correct Option: A. Solution: The energy of an electron in the nth orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} 	ext{ eV}$, where $n$ is the principal quantum number.

Question 28

Which of the following best explains why the hydrogen atom emits light of discrete wavelengths?

Accepted Answer

Correct Option: B. Solution: The hydrogen atom emits light of discrete wavelengths because the electron transitions between quantized energy levels, emitting photons with specific frequencies.

Question 29

In the Bohr model, which of the following statements about the electron in a hydrogen atom is correct when it transitions from $n=3$ to $n=2$?

Accepted Answer

Correct Option: A. Solution: When an electron transitions from a higher energy level to a lower one, it emits a photon with energy equal to the difference between the two levels, as per Bohr's third postulate.

Question 30

What happens when a hydrogen atom transitions from a higher energy state to a lower energy state?

Accepted Answer

Correct Option: B. Solution: When a hydrogen atom transitions from a higher energy state to a lower energy state, a photon is emitted with energy equal to the difference between the two states.

Question 31

In Bohr's model of the hydrogen atom, which postulate explains the quantization of angular momentum?

Accepted Answer

Correct Option: B. Solution: Bohr's second postulate states that the angular momentum of an electron is quantized and is an integral multiple of $\frac{h}{2\pi}$, where $h$ is Planck's constant.

Question 32

When a hydrogen atom is excited to its second excited state (n = 3), what is the energy required to ionize it from this state?

Accepted Answer

Correct Option: B. Solution: The energy of the second excited state (n = 3) is -1.51 eV. To ionize the atom from this state, the energy required is $0 \, 	ext{eV} - (-1.51 \, 	ext{eV}) = 1.51 \, 	ext{eV}$.

Question 33

In the context of hydrogen atom transitions, what is the significance of the equation $h
u = E_{ni} - E_{nf}$?

Accepted Answer

Correct Option: B. Solution: The equation $h
u = E_{ni} - E_{nf}$ represents the energy of a photon emitted when an electron transitions from a higher energy level $n_i$ to a lower energy level $n_f$ in a hydrogen atom.

Question 34

In the context of de Broglie's hypothesis, which of the following explains the quantization of angular momentum in Bohr's model?

Accepted Answer

Correct Option: C. Solution: De Broglie's hypothesis suggests that the quantization of angular momentum in Bohr's model arises because the electron's de Broglie wavelength forms standing waves, allowing only certain discrete orbits.

Question 35

According to Bohr's model, what happens when an electron transitions from a higher energy level to a lower energy level in a hydrogen atom?

Accepted Answer

Correct Option: B. Solution: When an electron transitions from a higher energy level to a lower energy level, a photon is emitted with energy equal to the difference between the two levels.

Question 36

According to de Broglie's hypothesis, what condition must be satisfied for an electron in a Bohr orbit to form a standing wave?

Accepted Answer

Correct Option: A. Solution: De Broglie proposed that the electron in its circular orbit must be seen as a particle wave, and standing waves are formed when the circumference of the orbit is an integral multiple of the de Broglie wavelength.

Question 37

What type of spectrum is emitted by rarefied gases when they are heated in a flame or excited electrically?

Accepted Answer

Correct Option: B. Solution: Rarefied gases emit discrete wavelengths forming a line spectrum, which appears as a series of bright lines.

Question 38

In Bohr's model, what happens when an electron transitions from a higher energy orbit to a lower energy orbit?

Accepted Answer

Correct Option: B. Solution: According to Bohr's third postulate, when an electron transitions from a higher energy orbit to a lower energy orbit, a photon is emitted with energy equal to the difference between the initial and final energy levels.

Question 39

In the Rutherford scattering experiment, what conclusion can be drawn from the observation that about 1 in 8000 alpha particles deflects by more than 90°?

Accepted Answer

Correct Option: C. Solution: The observation that a small fraction of alpha particles deflects by more than 90° suggests that the positive charge and most of the mass of the atom are concentrated in a small nucleus, providing a strong repulsive force.

Question 40

During the alpha-particle scattering experiment, what is the significance of the small fraction of alpha particles deflected at angles greater than 90 degrees?

Accepted Answer

Correct Option: B. Solution: The deflection of a small fraction of alpha particles at angles greater than 90 degrees indicates a strong repulsive force, confirming the presence of a small, dense, positively charged nucleus.

Question 41

Why is Bohr's model not applicable to multi-electron atoms?

Accepted Answer

Correct Option: B. Solution: Bohr's model does not account for the electron-electron interactions which are significant in multi-electron atoms.

Question 42

According to Bohr's model, what is the reason for the quantisation of angular momentum in hydrogen atoms?

Accepted Answer

Correct Option: A. Solution: Bohr's quantisation of angular momentum is explained by de Broglie's hypothesis that electrons exhibit wave nature, forming standing waves when the circumference of their orbit is an integral multiple of their wavelength.

Question 43

In the context of Rutherford's model, what would happen to an electron orbiting the nucleus according to classical electromagnetic theory?

Accepted Answer

Correct Option: B. Solution: According to classical electromagnetic theory, an accelerating electron should emit radiation, lose energy, and eventually spiral into the nucleus, which contradicts the stability of atoms.

Question 44

During a Rutherford scattering experiment, if the impact parameter is increased, what is the expected effect on the deflection of alpha particles?

Accepted Answer

Correct Option: B. Solution: Increasing the impact parameter means the alpha particles pass further from the nucleus, experiencing a weaker repulsive force, resulting in less deflection.

Question 45

What is the frequency of the photon emitted when an electron transitions from the n=3 to the n=2 level in a hydrogen atom?

Accepted Answer

Correct Option: B. Solution: The energy difference between the levels is $E_3 - E_2 = -1.51 	ext{ eV} - (-3.40 	ext{ eV}) = 1.89 	ext{ eV}$. The frequency of the emitted photon is given by $
u = \frac{E}{h}$, where $h = 6.626 	imes 10^{-34} 	ext{ Js}$. Converting $1.89 	ext{ eV}$ to joules gives $3.024 	imes 10^{-19} 	ext{ J}$. Thus, $
u = \frac{3.024 	imes 10^{-19}}{6.626 	imes 10^{-34}} = 6.17 	imes 10^{14} 	ext{ Hz}$.

Question 46

In the Bohr model of the hydrogen atom, what is the primary reason for the stability of the electron's orbit?

Accepted Answer

Correct Option: B. Solution: In the Bohr model, the stability of the electron's orbit is due to the quantization of angular momentum, which is an integral multiple of $\frac{h}{2\pi}$.

Question 47

Which of the following statements correctly describes a major failure of Rutherford's model of the atom?

Accepted Answer

Correct Option: A. Solution: Rutherford's model failed to explain why atoms emit light at only discrete wavelengths, contradicting the observed line spectra.

Question 48

In Bohr's model of the atom, which of the following statements is true regarding the electron's angular momentum?

Accepted Answer

Correct Option: A. Solution: In Bohr's model, the angular momentum of the electron is quantized and is given by $L = \frac{nh}{2\pi}$, where $n$ is the principal quantum number and $h$ is Planck's constant.

Question 49

Which of the following is a limitation of Bohr's model?

Accepted Answer

Correct Option: C. Solution: Bohr's model fails to explain the relative intensities of spectral lines and does not account for electron-electron interactions in multi-electron atoms.

Question 50

In the context of Bohr's model, how is the ionization energy of hydrogen defined?

Accepted Answer

Correct Option: B. Solution: The ionization energy of hydrogen is defined as the energy needed to remove an electron from the ground state to an infinitely far distance from the nucleus.

Question 51

In the context of the Plum Pudding Model, which experimental evidence led to its rejection?

Accepted Answer

Correct Option: B. Solution: The Plum Pudding Model was rejected after Rutherford's alpha-particle scattering experiment showed that a small fraction of alpha particles were deflected at large angles, indicating a concentrated positive charge in the nucleus.

Question 52

According to Bohr's model, what is the condition for the quantization of angular momentum for an electron orbiting the nucleus?

Accepted Answer

Correct Option: A. Solution: Bohr's second postulate states that the angular momentum of an electron in orbit is quantized and is given by $L = nh/2\pi$, where $n$ is an integer.

Question 53

What is the energy required to ionize a hydrogen atom from its ground state?

Accepted Answer

Correct Option: B. Solution: The ionization energy of hydrogen, which is the energy required to remove the electron from the ground state, is 13.6 eV.

Question 54

How would the results of the Rutherford scattering experiment change if a thin sheet of solid hydrogen was used instead of gold foil?

Accepted Answer

Correct Option: B. Solution: Hydrogen nuclei are much lighter than gold nuclei, so fewer alpha particles would experience significant deflection due to the smaller mass and charge of the hydrogen nucleus.

Question 55

Calculate the distance of closest approach for a 5.5 MeV alpha-particle in a gold foil experiment. Assume the atomic number of gold is 79.

Accepted Answer

Correct Option: B. Solution: Using the formula for distance of closest approach, $$d = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2Ze^2}{K}$$, where $Z = 79$, $e = 1.6 	imes 10^{-19} C$, $K = 5.5 	imes 10^{6} 	imes 1.6 	imes 10^{-13} J$, and $\frac{1}{4\pi\varepsilon_0} = 9.0 	imes 10^{9} N m^2/C^2$, we find $$d = 3.0 	imes 10^{-14} m$$.

Question 56

Which of the following statements correctly describes Thomson's Plum Pudding Model of the atom?

Accepted Answer

Correct Option: A. Solution: Thomson's Plum Pudding Model describes the atom as a spherical cloud of positive charges with electrons embedded in it, similar to seeds in a watermelon.

Question 57

In the context of atomic spectra, which of the following statements best describes the emission line spectra?

Accepted Answer

Correct Option: C. Solution: Emission line spectra consist of discrete wavelengths that are characteristic of each element, acting like a fingerprint for identification.

Question 58

According to De Broglie's hypothesis, what is the condition for the electron orbit to be a standing wave?

Accepted Answer

Correct Option: A. Solution: De Broglie's hypothesis states that the electron orbit is a standing wave when the circumference of the orbit is an integral multiple of the de Broglie wavelength, i.e., $2\pi r_n = n\lambda$.

Question 59

In the hydrogen spectrum, which series corresponds to transitions where the final energy level is $n=2$?

Accepted Answer

Correct Option: B. Solution: The Balmer series corresponds to electronic transitions in a hydrogen atom where the final energy level is $n=2$. These transitions are visible in the spectrum.

Question 60

According to Bohr's model of the hydrogen atom, which of the following transitions would result in the emission of a photon with the longest wavelength?

Accepted Answer

Correct Option: C. Solution: The longest wavelength corresponds to the smallest energy difference between levels. The energy difference decreases as the principal quantum number increases, hence the transition from $n=5$ to $n=4$ emits the longest wavelength.

Question 61

Which of the following statements best describes the limitation of Thomson's Plum Pudding Model in explaining atomic structure?

Accepted Answer

Correct Option: A. Solution: Thomson's Plum Pudding Model failed to explain the discrete spectral lines observed in atomic spectra, which was later addressed by Rutherford's model and Bohr's modifications.

Question 62

What is the significance of the negative sign in the total energy of an electron in a hydrogen atom according to Bohr's model?

Accepted Answer

Correct Option: A. Solution: The negative sign in the total energy indicates that the electron is bound to the nucleus and energy is required to remove it.

Question 63

What is one of the main failures of the Rutherford model of the atom?

Accepted Answer

Correct Option: C. Solution: Rutherford's model predicts that orbiting electrons would radiate energy and spiral into the nucleus, contradicting the observed stability of atoms and their line spectra.

Question 64

How does De Broglie's explanation support Bohr's quantization of angular momentum?

Accepted Answer

Correct Option: A. Solution: De Broglie's explanation supports Bohr's quantization of angular momentum by showing that only certain wavelengths can form standing waves, which corresponds to quantized orbits where $mv_nr_n = n\frac{h}{2\pi}$.

Atoms

Learning Objectives

Revision Notes & Summary

Chapter Twelve: Atoms

12.1 Introduction

12.2 Key Models of the Atom

Thomson's Model

Rutherford's Model

Bohr's Model

12.3 De Broglie's Explanation

12.4 Limitations of Bohr's Model

12.5 Summary of Key Points

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Multiple Choice Questions

Q1.Which of the following statements correctly describes the process of photon absorption in a hydrogen atom?

Correct Answer: B

Q2.What is the Bohr radius a0a_0a0​ for the ground state of hydrogen?

Correct Answer: A

Q3.In Bohr's model, what is the relationship between the angular momentum of an electron and Planck's constant?

Correct Answer: B

Q4.In the Geiger-Marsden experiment, what was the primary observation that led to the conclusion of a small, dense atomic nucleus?

Correct Answer: A

Q5.In the context of the Geiger-Marsden experiment, what is the significance of the distance of closest approach for an alpha particle?

Correct Answer: B

Q6.In the context of atomic spectra, which of the following transitions would result in the emission of a photon?

Correct Answer: A

Q7.What is the energy required to ionize a hydrogen atom from its ground state?

Correct Answer: A

Q8.In the context of the hydrogen atom, what does a negative total energy indicate about the electron's state?

Correct Answer: B

Q9.In the Geiger-Marsden experiment, what was the primary observation that led to the conclusion of a dense nucleus?

Correct Answer: B

Q10.If the alpha-particle scattering experiment were conducted with a thin sheet of solid hydrogen instead of gold, what would be the expected outcome?

Correct Answer: B

Q11.In the context of Rutherford's experiment, if an alpha-particle is observed to scatter at a large angle, what can be inferred about its impact parameter?

Correct Answer: B

Q12.Consider a hydrogenic atom with a nucleus of charge +Ze+Ze+Ze and a single electron. According to Bohr's model, what is the expression for the radius of the electron's orbit in the nthn^{th}nth energy level?

Correct Answer: A

Q13.If an electron in a hydrogen atom transitions from the n = 3 state to the n = 2 state, what is the energy of the photon emitted?

Correct Answer: A

Q14.According to Bohr's model, which of the following transitions will result in the emission of a photon with the highest energy?

Correct Answer: C

Q15.In the context of atomic spectra, what happens when a photon with energy equal to the difference between two energy levels is absorbed by an atom?

Correct Answer: B

Q16.In Rutherford's nuclear model of the atom, what is the primary reason most alpha particles pass through the gold foil with little or no deflection?

Correct Answer: B

Q17.Which of the following statements best explains why Bohr's model cannot be extended to multi-electron atoms?

Correct Answer: A

Q18.Which of the following statements about the alpha-particle scattering experiment is true?

Correct Answer: B

Q19.According to Bohr's second postulate, the angular momentum of an electron in a stable orbit is quantized. Which of the following expressions correctly represents this quantization?

Correct Answer: A

Q20.In Bohr's model, when an electron transitions from a higher energy orbit to a lower energy orbit, a photon is emitted. What is the relationship between the energy of the photon and the initial and final energy states of the electron?

Correct Answer: B

Q21.According to Rutherford's nuclear model, what is the approximate size of the nucleus compared to the size of the atom?

Correct Answer: B

Q22.Which of the following correctly describes the process that occurs when an atom absorbs a photon?

Correct Answer: C

Q23.In the Bohr model of the hydrogen atom, what is the significance of the quantization of angular momentum?

Correct Answer: B

Q24.Which of the following statements best describes the significance of the impact parameter in the Rutherford scattering experiment?

Correct Answer: C

Q25.What does the Rutherford model fail to explain about the atomic structure?

Correct Answer: B

Q26.In Bohr's model, what happens when an electron transitions from a higher energy state to a lower energy state?

Correct Answer: C

Q27.In the Bohr model of the hydrogen atom, what is the expression for the energy of an electron in the nth orbit?

Correct Answer: A

Q28.Which of the following best explains why the hydrogen atom emits light of discrete wavelengths?

Correct Answer: B