Choose the correct alternative from the clues given at the end of the each statement: (I) The size of the atom in Thomson’smodelisthe atomic size inRutherford’s model. (much greater than/no different from/much less than.) (II) Inthegroundstateof..........electronsareinstableequilibrium,whilein.......... electrons always experience a net force. (Thomson’s model/ Rutherford’s model.) (III) A classical atombasedonis doomed tocollapse. (Thomson’s model/ Rutherford’s model.) (IV) An atom has a nearly continuous mass distributioninabut has a highlynon- uniform mass distribution in .......... (Thomson’s model/ Rutherford’s model.) (V) The positively charged part of the atom possesses most of the mass in.......... (Rutherford’s model/both the models.)

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

What is the shortest wavelength present in the Paschen series of spectral lines?

A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and potential energies of the electron in this state?

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n= 4 level. Determine the wavelength and frequency of the photon.

(a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.

The radius of the innermost electron orbit of a hydrogen atom is 5.3 ×10^-11 m. What are the radii of the n = 2 and n =3 orbits?

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5 × 10¹¹ m with orbital speed 3× 104 m/s. (Mass of earth = 6.0 × 1024 kg.)

The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10^-40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de- excites from level n to level (n-1). For large n, show that this frequency equals the classical frequency of revolution of the electron in the orbit.

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 nature 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^-10 m). (I) Constructaquantitywiththedimensionsoflengthfromthefundamentalconstants e, m_e, and c. Determine its numerical value. (II) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativisticdomainwherecisnotexpectedtoplayanyrole.Thisiswhatmayhave suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now,thePlanck’sconstanthhadalreadymadeitsappearanceelsewhere.Bohr’sgreat insight 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, m_e, and e and confirm that its numerical value has indeed the correct order ofmagnitude.

The total energy of an electron in the first excited state of the hydrogen atom is about -3.4 eV. (I) What is the kinetic energy of the electron in thisstate? (II) What is the potential energy of the electron in thisstate? (III) Whichoftheanswersabovewouldchangeifthechoiceofthezeroofpotential energy ischanged?

If Bohr’s quantisation postulate (angular momentum = nh/2p) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?

ObtainthefirstBohr’sradiusandthegroundstateenergyofamuonichydrogenatom [i.e., an atom in which a negatively charged muon (µ^-) of mass about 207m_e orbits around aproton].