What is the velocity of electron present in first Bohr orbit of hydrogen atom? (a) \(2.18 \times 10^{5} \mathrm{~m} / \mathrm{s}\) (b) \(2.18 \times 10^{6} \mathrm{~m} / \mathrm{s}\) (c) \(2.18 \times 10^{-18} \mathrm{~m} / \mathrm{s}\) (d) \(2.18 \times 10^{-9} \mathrm{~m} / \mathrm{s}\)

Understanding the velocity of an electron within an atom is a key concept in comprehending how atoms behave. In Bohr's Model, the electron velocity is highly predictable due to the quantized nature of orbits, which is a departure from classical views of electron motion.

For the first Bohr orbit of the hydrogen atom, for instance, the velocity can be determined using the formula \(v_n = \frac{e^2}{2h} \cdot \frac{1}{n}\), where \(v_n\) represents the electron velocity, \(n\) is the principal quantum number, \(e\) is the elementary charge, and \(h\) is Planck's constant. For the n=1 orbit, the electron velocity is found to be approximately \(2.18 \times 10^6 \mathrm{~m} / \mathrm{s}\), which reveals the electron’s high speed on the microscopic scale.

Through exercises like this, students can gain a better grasp of the precise and unique behaviors of subatomic particles, a key understanding in the study of atomic physics.

Bohr orbits are specific paths around the nucleus where electrons are found in an atom according to Bohr's Model. These orbits correspond to certain energy levels, and they are quantized, meaning that electrons can only occupy particular orbits with defined radii and energy, not anywhere in between.

For instance, the formula for the radius of the nth Bohr orbit is \(r_n = \frac{n^2h^2}{4\pi^2me^2}\), where \(n\) is the principal quantum number, \(h\) is Planck's constant, \(m\) is the electron mass, and \(e\) is the elementary charge. This model successfully explains the stability of atoms and their emission spectra. Moreover, the quantization of the orbits gives rise to the concept of 'quantum jumps', where electrons can jump between orbits while absorbing or emitting energy.

Quantum mechanics is the branch of physics that studies the behavior of energy and matter at the atomic and subatomic levels. It is the foundation upon which the Bohr Model of the atom was developed. Unlike classical mechanics that describe the physical world we experience directly, quantum mechanics reveals a world where probability and uncertainty are intrinsic qualities.

Within quantum mechanics, concepts like the wave-particle duality and the Heisenberg Uncertainty Principle challenge our classical notions. Particles like electrons exhibit both particle-like and wave-like behavior. Quantum mechanics, with its mathematical framework, allows us to calculate properties such as the positions, velocities, and energies of particles with a certain probability, rather than with absolute certainty. The introduction to these principles through Bohr's Model sets the stage for deeper exploration into quantum theories and how they shape our understanding of the very fabric of reality.