Explanation: This question examines the scientific idea that helped Bohr improve Rutherford’s atomic model and explain atomic stability more successfully. Earlier atomic theories could not clearly describe why electrons remained stable around the nucleus or why atoms produced fixed spectral lines. Understanding the historical development of Atomic Structure is important for connecting classical Physics with modern quantum concepts.
Rutherford’s model successfully described the existence of a dense nucleus but failed to explain why orbiting electrons do not continuously lose energy and collapse into the nucleus. Bohr introduced a new approach inspired by early quantum ideas. He proposed that electrons move only in certain permitted orbits with fixed energies. In these orbits, electrons remain stable and do not radiate energy continuously. energy exchange occurs only when electrons move between allowed energy levels. This idea explained the discrete line Spectrum observed experimentally for hydrogen atoms and solved many difficulties faced by classical theories.
A useful comparison is a staircase and a ramp. A ramp allows movement through every possible position, while a staircase permits only fixed steps. Similarly, electrons in Bohr’s model occupy only specific energy levels rather than any random orbit.
The explanation highlights how Bohr combined nuclear structure with early quantum principles to build a more successful atomic model that explained atomic stability and spectral observations.
Option c - Planck’s quantum theory
According to Bohr’s postulates, an electron present in a selected quantum orbit:
Explanation: This question focuses on one of the central ideas proposed in Bohr’s atomic theory regarding the behavior of electrons inside an Atom. Classical electromagnetic theory predicted that moving charged particles should continuously radiate energy. If this happened inside atoms, electrons would gradually spiral into the nucleus, making atoms unstable. Bohr introduced a new concept to resolve this contradiction.
According to Bohr, electrons are allowed to revolve around the nucleus only in certain permitted orbits known as stationary states. While moving in these specific orbits, electrons maintain fixed energy values and remain stable. Energy transfer does not occur during ordinary motion inside a permitted orbit. Instead, energy is exchanged only when an electron jumps from one allowed orbit to another. During such transitions, energy may appear as absorbed or emitted radiation depending on the direction of movement between energy levels.
An everyday analogy is a train moving smoothly on fixed Railway tracks without losing energy because of wandering motion. The train changes energy conditions only when shifting tracks or changing speed, similar to electron transitions between orbits.
The discussion emphasizes how Bohr’s postulates solved the stability problem of atoms and explained the appearance of discrete atomic spectra observed experimentally.
Option d - Neither absorbs nor emits energy
As per Bohr’s atomic theory, the angular momentum of an electron in an allowed orbit is proportional to the:
a) Inverse of the principal quantum number
b) Square of the principal quantum number
c) Cube of the principal quantum number
d) Principal quantum number
Explanation: This question explores one of the major postulates introduced in Bohr’s atomic model regarding the motion of electrons around the nucleus. Classical Physics allowed electrons to possess any arbitrary value of angular momentum, but Bohr proposed that only certain fixed values are permitted. This idea introduced quantization into Atomic Structure and became an important step toward modern quantum mechanics.
Bohr suggested that the angular momentum of an electron is not continuous but exists only in specific discrete amounts. These allowed values depend on a number associated with the orbit, commonly called the principal quantum number. As the orbit number increases, the angular momentum also changes in a regular pattern. This restriction explains why electrons occupy only particular stable orbits instead of moving randomly around the nucleus. The quantization condition successfully accounted for the observed spectral lines of hydrogen and helped explain atomic stability.
An analogy can be taken from climbing stairs. A person may stand only on specific steps and not between them. Similarly, electrons can possess only certain permitted angular momentum values rather than every possible value.
The concept demonstrates how Bohr combined classical circular motion with quantum restrictions to explain the arrangement and behavior of electrons inside atoms.
Option d - Principal quantum number
In Bohr’s model, which physical quantity is quantized and can exist only in integral multiples of h/27 is?
a) Angular momentum
b) Linear momentum
c) Energy–momentum
d) Quantum frequency
Explanation: This question highlights the concept of quantization introduced by Bohr in his atomic theory. In classical mechanics, physical quantities such as momentum or energy can usually vary continuously. However, Bohr proposed that certain properties of electrons inside atoms are restricted to fixed discrete values. This marked a major shift from classical Physics to early quantum theory.
Bohr applied the idea that electrons revolve around the nucleus only in selected stable orbits. For these orbits to exist, a particular physical quantity related to rotational motion must satisfy a fixed mathematical condition involving Planck’s constant. This means the quantity can take only integral multiples of a basic unit and cannot vary continuously. Because of this restriction, electrons remain stable in fixed orbits and atoms produce discrete spectral lines instead of continuous radiation. The proposal successfully explained experimental observations related to hydrogen spectra.
A simple comparison is tuning a musical instrument. Only certain notes produce stable harmonies, while intermediate sounds may not fit properly. Likewise, electrons occupy only certain permitted rotational states inside atoms.
The discussion shows how Bohr introduced quantized rotational behavior to explain atomic stability and the existence of sharply defined spectral lines.
Option a - Angular momentum
Bohr’s atomic model gained acceptance mainly because it successfully explained:
Explanation: This question focuses on the major achievement that made Bohr’s atomic theory scientifically important and widely accepted. Earlier atomic models described some structural features of atoms but failed to explain important experimental observations. Scientists especially struggled to understand why atoms emitted Light only at certain specific wavelengths instead of producing a continuous range of colors.
Bohr proposed that electrons revolve around the nucleus only in fixed energy levels. When an electron shifts between these levels, energy is emitted or absorbed in definite amounts. Because only certain transitions are possible, atoms produce Light with particular wavelengths instead of continuous radiation. This idea matched the experimentally observed spectral lines of hydrogen very accurately. The success of the theory in explaining atomic spectra gave strong support to the concept of quantized energy levels and established Bohr’s model as a major advancement in atomic Physics.
An everyday example is a piano keyboard. Pressing specific keys produces fixed musical notes rather than every possible sound frequency. Similarly, atoms emit only certain allowed wavelengths of Light.
The explanation emphasizes that Bohr’s theory became important because it connected Atomic Structure with experimentally observed spectral behavior in a mathematically successful way.
Option c - The experimentally observed hydrogen Spectrum
Bohr modified Rutherford’s atomic model by introducing the condition that:
Explanation: This question examines the central modification Bohr made to Rutherford’s atomic theory. Rutherford’s model successfully explained the existence of a positively charged nucleus but faced a major problem concerning electron stability. According to classical electromagnetic theory, moving electrons should continuously lose energy and eventually collapse into the nucleus, making atoms unstable.
To overcome this difficulty, Bohr proposed that electrons cannot revolve in just any orbit around the nucleus. Instead, they are restricted to certain specific permitted paths having fixed energies. While moving in these allowed orbits, electrons do not continuously radiate energy. Energy exchange takes place only when electrons move between one permitted orbit and another. This condition introduced the idea of quantized energy levels and helped explain why atoms remain stable and why they emit discrete spectral lines.
A useful analogy is vehicles traveling only on designated lanes of a highway. Cars remain orderly and controlled because movement is restricted to fixed paths rather than random directions.
The explanation shows how Bohr strengthened Rutherford’s nuclear model by introducing restricted electron orbits, which solved the instability problem and explained atomic spectral observations.
Option b - Electrons are restricted to specific permitted orbits
While formulating his atomic theory, Bohr applied the principle of conservation of:
a) Angular momentum
b) Linear momentum
c) Energy–momentum
d) Quantum frequency
Explanation: This question deals with an important physical principle used by Bohr while developing his atomic model. In Physics, conservation laws help describe quantities that remain constant during motion or interaction. Bohr combined classical mechanics with early quantum ideas to explain how electrons revolve around the nucleus in stable and well-defined paths.
In circular motion, electrons possess a rotational property connected with their Mass, velocity, and orbital radius. Bohr proposed that this quantity follows special restrictions and remains associated with stable orbital motion. By combining classical conservation ideas with quantization conditions, he derived expressions for allowed radii and energies of electrons in atoms. These calculations successfully explained the hydrogen Spectrum and established a connection between Atomic Structure and measurable physical properties.
A spinning ice skater provides a simple analogy. As the skater changes position, rotational motion follows certain predictable rules that remain consistent. Similarly, electron motion inside atoms obeys well-defined rotational principles.
The discussion demonstrates how Bohr relied on conservation concepts together with quantization to build a stable and mathematically successful model of Atomic Structure and electron motion.
Option a - Angular momentum
According to Bohr’s model, an electron can revolve steadily around the nucleus only if it moves in a:
a) Continuously expanding orbit
b) Gradually shrinking orbit
c) Orbit of fixed but arbitrary radius
d) Allowed or quantized orbit
Explanation: This question examines the condition required for stable electron motion in Bohr’s atomic theory. Classical Physics suggested that orbiting electrons should continuously lose energy because accelerating charges emit radiation. If this occurred inside atoms, electrons would gradually spiral into the nucleus, causing atomic collapse. Bohr introduced a new idea to solve this instability problem.
Bohr proposed that electrons can revolve around the nucleus steadily only in certain special orbits having fixed energies. These orbits are called allowed or quantized orbits. Inside such paths, electrons neither gain nor lose energy during normal motion. Radiation occurs only when electrons shift between different permitted energy levels. Because only specific orbits are allowed, atoms remain stable and produce discrete spectral lines instead of continuous radiation. This concept became one of the foundations of early quantum theory.
An analogy can be made with trains running on fixed Railway tracks. The train moves smoothly and predictably only while staying on the permitted track path.
The explanation highlights how Bohr introduced restricted stable orbits to explain both atomic stability and the experimentally observed behavior of atomic spectra.
Option d - Allowed or quantized orbit
With an increase in the radius of an electron’s orbit:
a) Kinetic energy decreases and potential energy increases
b) Kinetic energy increases and potential energy decreases
c) Both kinetic and potential energies decrease
d) Both kinetic and potential energies increase
Explanation: This question focuses on how different forms of energy change when an electron moves to an orbit farther from the nucleus in Bohr’s atomic model. Electrons revolving around the nucleus possess both kinetic energy due to motion and potential energy due to electrostatic attraction between opposite charges. The balance between these energies determines the stability of the orbit.
When the orbital radius increases, the electron moves farther away from the attractive pull of the nucleus. Because the electrostatic force becomes weaker at larger distances, the electron requires less speed to maintain circular motion. As a result, its kinetic energy decreases. At the same time, the potential energy becomes less negative and effectively increases because the attraction between the nucleus and electron weakens with distance. These energy variations are important in understanding electron transitions and atomic spectra.
A simple analogy is a satellite moving farther from Earth. At greater distances, gravitational attraction weakens, reducing the speed needed to remain in orbit while changing the satellite’s energy conditions.
The discussion explains how increasing orbital distance changes the balance between motion-related energy and electrostatic potential energy inside atoms.
Option a - Kinetic energy decreases and potential energy increases
If the time period of an electron in the first Bohr orbit is T, then the time period in the second orbit is:
a) 8T
b) 4T
c) 2T
d) T/8
Explanation: This question deals with the relationship between orbital motion and the size of electron orbits in Bohr’s atomic theory. The time period represents the duration required for an electron to complete one full revolution around the nucleus. In Bohr’s model, quantities such as orbital radius and electron speed depend systematically on the principal quantum number.
As electrons move to higher orbits, the orbital radius increases significantly while the electron speed changes differently. The time period depends on both the circumference of the orbit and the speed of the electron. Since larger orbits require electrons to travel a greater distance, the time required for one complete revolution changes according to mathematical relations derived from Bohr’s equations. Understanding these proportional relationships helps explain the structure of atomic motion and energy levels.
An analogy can be taken from athletes running on circular tracks. A runner on a larger outer track covers a longer distance during one lap and usually takes more time to complete the revolution.
The explanation emphasizes how orbital size and electron speed together determine the revolution time of electrons in different Bohr orbits within atoms.
Option a - 8T
An electron revolving around the nucleus possesses:
a) Only potential energy
b) Only kinetic energy
c) Both kinetic and potential energy
d) Zero energy
Explanation: This question examines the different forms of energy associated with an electron moving around the nucleus in an Atom. In Bohr’s model, the electron behaves like a particle in circular motion while also experiencing electrostatic attraction toward the positively charged nucleus. Because of these conditions, more than one form of energy becomes important in describing Atomic Structure.
The moving electron possesses kinetic energy because of its velocity while revolving around the nucleus. At the same time, the attractive electrostatic force between the negatively charged electron and positively charged nucleus creates potential energy. The total energy of the electron depends on the combination of these two forms of energy. Their relationship determines the stability of the orbit and the energy changes involved when electrons move between different energy levels. These concepts are fundamental for understanding atomic spectra and electron transitions.
A useful analogy is a planet orbiting the Sun. The planet has kinetic energy because of motion and gravitational potential energy because of its position in the gravitational field.
The discussion explains that electron motion inside atoms involves a combination of motion-related and interaction-related energies that together define atomic behavior and stability.
Option c - Both kinetic and potential energy
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