The extent of localisation of a particle is determined roughly by its de-Broglie wave.If an electron is loclalized within the nucleus (of size about 10^(-14)m) of an atom,what is its energy?Compare this energy with the typicla binding energyies(of the order of a few Me) in a nucleus and hyence argue why electrons cannot reside in a nucleus.

classically an electron can be in any orbit around nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? Thequestion had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as followswith the basic constants of nature e, me, c and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10 m).- You will find that the length obtained above is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for else h had already made its appearance elsewhere. Bohr lay in recognising that h, m_e , and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.

Bohr's model of hydrogen atom In order to explain the stability of atom and its line spectra, Bohr gave a set of postulates: An electron in an atom revolves in certain circular orbit around the nucleus. These are the orbits for which mvr=(nh)/(2pi) In these allowed orbits, the electron does not radiate energy. When an electron jumps from higher energy level E_(n_2) to lower energy orbit E_(n_1) , radiation is emittd and frequency of emitted electron is given by v=(E_(n_2)-E_(n_1))/h . Further the radius of the n^(th) orbit of hydrogen atom is r=(n^2h^24piepsilon_0)/(4pi^2me^2) and energy of the n^(th) orbit is given by E_n=-13.6/n^2 eV . If 13.6 eV energy is required to ionise the hydrogen atom, then enegy required to remove an electron from n=2 is:

Bohr's model of hydrogen atom In order to explain the stability of atom and its line spectra, Bohr gave a set of postulates: An electron in an atom revolves in certain circular orbit around the nucleus. These are the orbits for which mvr=(nh)/(2pi) In these allowed orbits, the electron does not radiate energy. When an electron jumps from higher energy level E_(n_2) to lower energy orbit E_(n_1) , radiation is emittd and frequency of emitted electron is given by v=(E_(n_2)-E_(n_1))/h . Further the radius of the n^(th) orbit of hydrogen atom is r=(n^2h^24piepsilon_0)/(4pi^2me^2) and energy of the n^(th) orbit is given by E_n=-13.6/n^2 eV . The ground state energy of hydroen atom is -13.6 eV. The KE and PE of the electron in this state are

Bohr's model of hydrogen atom In order to explain the stability of atom and its line spectra, Bohr gave a set of postulates: An electron in an atom revolves in certain circular orbit around the nucleus. These are the orbits for which mvr=(nh)/(2pi) In these allowed orbits, the electron does not radiate energy. When an electron jumps from higher energy level E_(n_2) to lower energy orbit E_(n_1) , radiation is emittd and frequency of emitted electron is given by v=(E_(n_2)-E_(n_1))/h . Further the radius of the n^(th) orbit of hydrogen atom is r=(n^2h^24piepsilon_0)/(4pi^2me^2) and energy of the n^(th) orbit is given by E_n=-13.6/n^2 eV . What would happen, if the electron in an atom is stationary?

Bohr's model of hydrogen atom In order to explain the stability of atom and its line spectra, Bohr gave a set of postulates: An electron in an atom revolves in certain circular orbit around the nucleus. These are the orbits for which mvr=(nh)/(2pi) In these allowed orbits, the electron does not radiate energy. When an electron jumps from higher energy level E_(n_2) to lower energy orbit E_(n_1) , radiation is emittd and frequency of emitted electron is given by v=(E_(n_2)-E_(n_1))/h . Further the radius of the n^(th) orbit of hydrogen atom is r=(n^2h^24piepsilon_0)/(4pi^2me^2) and energy of the n^(th) orbit is given by E_n=-13.6/n^2 eV . The angular momentum of the orbital electron is integarl multiple of

Bohr's model of hydrogen atom In order to explain the stability of atom and its line spectra, Bohr gave a set of postulates: An electron in an atom revolves in certain circular orbit around the nucleus. These are the orbits for which mvr=(nh)/(2pi) In these allowed orbits, the electron does not radiate energy. When an electron jumps from higher energy level E_(n_2) to lower energy orbit E_(n_1) , radiation is emittd and frequency of emitted electron is given by v=(E_(n_2)-E_(n_1))/h . Further the radius of the n^(th) orbit of hydrogen atom is r=(n^2h^24piepsilon_0)/(4pi^2me^2) and energy of the n^(th) orbit is given by E_n=-13.6/n^2 eV . When hydrogen atom is the first excited level, it radius is:,

The nucleus of an atom of ._(92)Y^(235) initially at rest decays by emitting an alpha particle. The binding energy per nucleon of parent and dougther nuclei are 7.8MeV and 7.835MeV respectively and that of alpha particles is 7.07MeV//"nucleon". Assuming the dougther nucleus to be formed in the unexcited state and neglecting its share of energy in the reaction, calculate speed of emitted alpha particle. Take mass of alpha particle to be 6.68xx10^(-27)kg .

Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of and see if we can get a quantity with the dimensions of length that is roughly equal to the known of an atom (~ 10^ -10 m).- Construct a quantity with the dimensions of length from the fundamental constants e, m_e , and c. Determine its numerical value.

An electron is circulating around the nucleus of a hydrogen ato in a circular orbit of radius 5.3 cxx10^-11 m. Calculate the electric potential energy of the atom in eV. What would be the electric potential due to a helium nucleus at the same radius. Given, that (4piepsilon_0)^-1 = 9xx10^9 m F^-1 and e = 1.6 xx 10^-19 C .

The binding energy of a H-atom, considering an electron moving around a fixed nucleus (proton), is B=-(me^4)/(8n^2epsilon_0^2h^2) (m=electron mass) If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be B=-(me^4)/(8n^2epsilon_0^2h^2) (M=proton mass). This last expression is not correct because.