The radius of 8 orbit of electron in h atom will be more than that of 4th orbit by a factor of

• Neil Bohr gave a model of the atom. • According to Neil Bohr, each shell of the atom has some amount of energy, therefore he gave another name for the shell is energy levels and an electron will revolve only in that orbit where its energy remains conserved. • Neil Bohr chose the hydrogen atom for his theory and he also gave the formula to calculate the radius of an orbit. • The formula to calculate the atomic radius is r = ( 0 . 0529 ) n 2 Z. Where n is the number of orbits and z is the atomic number of atoms. • Hydrogen has the atomic number 1. Calculation. Here, we have to calculate the radius for the fifth orbit of the hydrogen atom = 0 . 0529 × ( 5 ) 2 1 = 0 . 0529 × 25 = 1 . 3225 nm The Bohr's radius for the fifth orbit of the hydrogen atom is 1 . 3225 nm

\( \newcommand\) • • • • • • • • • • • • • • Learning Objectives • To know the relationship between atomic spectra and the electronic structure of atoms. The concept of the photon emerged from experimentation with thermal radiation, electromagnetic radiation emitted as the result of a source’s temperature, which produces a continuous spectrum of energies.The photoelectric effect provided indisputable evidence for the existence of the photon and thus the particle-like behavior of electromagnetic radiation. However, more direct evidence was needed to verify the quantized nature of energy in all matter. In this section, we describe how observation of the interaction of atoms with visible light provided this evidence. Line Spectra Although objects at high temperature emit a continuous spectrum of electromagnetic radiation, a different kind of spectrum is observed when pure samples of individual elements are heated. For example, when a high-voltage electrical discharge is passed through a sample of hydrogen gas at low pressure, the resulting individual isolated hydrogen atoms caused by the dissociation of H 2 emit a red light. Unlike blackbody radiation, the color of the light emitted by the hydrogen atoms does not depend greatly on the temperature of the gas in the tube. When the emitted light is passed through a prism, only a few narrow lines of particular wavelengths, called a line spectrum, are observed rather than a continuous range of wavelengths (Figure \(\PageIndex \] w...

Let, m e = mass of electron, −e = charge on electron, r n = radius of nth Bohr’s orbit, +e = charge on nucleus, v n = linear velocity of electron in n th orbit, Z = number of electrons in an atom, n = principal quantum number. ∴ The angular momentum = m ev nr n According to second postulate. m ev nr n= `"nh"/("2"pi)` ...(i) From Bohr’s first postulate, Centripetal force = Electrostatic force ∴ `("m"_"e""v"_"n"^2)/"r"_"n" = "Ze"^2/(4piepsilon_0"r"_"n"^2)` ∴ `"v"_"n"^2 = "Ze"^2/(4piepsilon_0"r"_"n""m"_"e")` ....(ii) Squaring equation (i) we get `"m"_"e"^2 "v"_"n"^2 "r"_"n"^2 = ("n"^2"h"^2)/(4pi^2)` ∴ `"v"_"n"^2 = ("n"^2"h"^2)/(4pi^2"m"_"e"^2"r"_"n"^2)` ….(iii) Equating equations (ii) and (iii), we get, `("n"^2"h"^2)/(4pi^2"m"_"e"^2"r"_"n"^2) = "Ze"^2/(4piepsilon_0"r"_"n""m"_"e")` ∴ r n = `("n"^2"h"^2epsilon_0)/(pi"m"_"e""Z"_"e"^2)` This is the required expression for radius of n th Bohr orbit of the electron.

L is defined to be r x p, which is r*p*sin(theta), where theta is the angle between the radius vector and the momentum vector. Since they are moving in a circle, that means that p and r are perpendicular, so sin(theta) is just 1, leaving rp. Since p is just mv, that means that L=mvr. The way he arrived at the conclusion L=nh/2pi is experimentally. The predicted emission spectrum of Hydrogen would not agree with reality unless he quantized L like that. Bohr and the science community at the time already knew that energy from the H atom was emitted at specific, discrete values (referred to as the wavelength or frequency of the emitted light energy). He and his mentor, Rutherford, had already conceived of the "orbital model" of atoms (as opposed to the earlier plum pudding model where all electrons and and protons are mixed together in the nucleus like raisins in a pudding). So, based on these he took an insightful hypothesis that the orbits that the electrons were in were orbits that were in incremental, or quantum if you prefer, steps. So his hypothesis involved asserting that the electrons were in an orbital distance of 1 radius, or 2 radii or 3 radii from the nucleus. It was an ingenious insight, but a hypothesis is an educated guess based on the observations. He needed to express it mathematically and compare that mathematical result with the observations of the energy emissions. Like many hypotheses, it worked very well to describe the phenomena in a set of instances, bu...

Learning Objectives • To know the relationship between atomic spectra and the electronic structure of atoms. In 1913, a Danish physicist, Niels Bohr (1885–1962; Nobel Prize in Physics, 1922), proposed a theoretical model for the hydrogen atom that explained its emission spectrum. Bohr’s model required only one assumption: The electron moves around the nucleus in circular orbits that can have only certain allowed radii. Rutherford’s earlier model of the atom had also assumed that electrons moved in circular orbits around the nucleus and that the atom was held together by the electrostatic attraction between the positively charged nucleus and the negatively charged electron. Although we now know that the assumption of circular orbits was incorrect, Bohr’s insight was to propose that the electron could occupy only certain regions of space. Using classical physics, Niels Bohr showed that the energy of an electron in a particular orbit is given by \[ E_\) The Bohr Model of the Hydrogen Atom (a) The distance of the orbit from the nucleus increases with increasing n. (b) The energy of the orbit becomes increasingly less negative with increasing n. Niels Bohr (1885–1962) During the Nazi occupation of Denmark in World War II, Bohr escaped to the United States, where he became associated with the Atomic Energy Project. In his final years, he devoted himself to the peaceful application of atomic physics and to resolving political problems arising from the development of atomic weapon...

Description In atomic physics, the Rutherford–Bohr model or Bohr model, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus. The electrons can only orbit stably, without radiating, in certain orbits at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron’s acceleration does not result in radiation and energy loss as required by classical electromagnetics. Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency determined by the energy difference of the levels. The allowed electron’s orbit radius at any level “n” is related to electron’s orbit number, electron’s mass, electron’s charge and the atom’s atomic number.