Ambedkar Nagar

Prime Classes for IIT-JEE/PMT, Ambedkar nagar

1. Calculate the wavelength of light radiation that would be emitted, when an electron in the fourth Bohrsorbit of He+ ion falls to the second Bohrs orbit. To what transition does this light radiation correspond in theH-atom ?

2. Find the wavelength of radiation required to excite the electron in ground level of Li++ (Z = 3) to third energylevel. Also find the ionisation energy of Li2+ .

3. Calculate the uncertainty in position assuming uncertainty in momentum within 0.1 % for :a. A tennis ball weighing 0.2 kg and moving with a velocity of 10 m/s.b. An electron moving in an atom with a velocity of 2 106 m/s.

4. Find out the number of waves made by a Bohr electron in one complete revolution in its 3rd orbit.5. Find the energy released (in ev), when 2.0 gm atom of Hydrogen undergo transition giving spectral line of

lowest energy in visible region of its atomic spectrum.6. Hydrogen like atom (described by the Bohrs model) is observed to emit six wavelengths, originating from all

possible transitions between a group of levels. These levels have energies between 0.85 eV and 0.544 eVincluding both these values).

a. Find the atomic number of the atom.b. Calculate the smallest wavelength emitted in these transitions.

7. Electrons in hydrogen like atom (Z = 3) make transition from the fifth to the fourth orbit and from the fourthto the third orbit. The resulting radiations are incident normally on a metal plate and eject photoelectrons.The stopping potential for the photo-electrons ejected by the shorter wavelength is 3.95 eV. Calculate thework function of the metal and stopping potential for the photo-electrons ejected by the longer wavelength.

8. Estimate the difference in energy between 1st and 2nd Bohrs orbit for a H atom. At what minimum atomicnumber a transition from n = 2 to n = 1 energy level would result in the emission of X-rays with = 3.0 108

m? Which hydrogen atom like species does this atomic number corresponds to?9. When a beam of 10.6 eV photons of intensity 2.0 W/m2 falls on a platinum surface of area 1 10-4 m2 and

work function 5.6 eV , 0.53 % of the incident photons eject photo electrons. Find the number of photo electrons emitted per second and their minimum energies in (eV). Take 1 eV = 1.6 10-19 J .

10. Assume that the de Broglie wave associated with an electron can form a standing wave between the atomsarranged in a one dimensional array with nodes at each of the atomic sites . It is found that one suchstanding wave is formed if the distance d between the atoms of the array is 2 . A similar standing wave isagain formed if d is increased to 2.5 but not for any intermediate value of d . Find the energy of theelectrons in electron volts and the least value of d for which the standing wave of the type described can beformed.

11. The electron energy in hydrogen atom is given by En = -13.6/n2 eV. Calculate the energy required to removean electron completely from n = 2 orbit. What is the largest wavelength in cm of light that can be used tocause this transition?

12. Electrons of energy 12.09 eV can excite hydrogen atoms. To which orbit is the electron in the hydrogen atomraised and what are the wavelengths of the radiations emitted as it drops back to the ground state?

13. One mole He+ ions are excited. Spectral analysis showed existence of 50% ions in 3rd orbit, 25% in 2nd andrest in ground state. Calculate total energy evolved when all the ions return to the ground state.

14. The energy of an excited H-atom is -3.4 eV. Calculate angular momentum of e-.

Prime Classes for IIT-JEE/PMT, Ambedkar nagar

Bohr's Model-XI

UPS 1

Ambedkar Nagar

Prime Classes for IIT-JEE/PMT, Ambedkar nagar

15. The hydrogen atom in the ground state is excited by means of monochromatic radiation of wavelength xA.The resulting spectrum consists of 15 different lines. Calculate the value of x.

16. Calculate the frequency of e- in the first Bohr orbit in an H-atom.17. A single electron orbits around a stationary nucleus of charge +Ze where Z is a constant from the nucleus and

e is the magnitude of the electric charge. The hydrogen like species required 47.2 eV to excite the electronfrom the second Bohr orbit to the third Bohr orbit. Find

a. the value of Z and give the hydrogen like species formed.b. the kinetic energy and potential energy of the electron in the first Bohr orbit.

18. A stationary He+ ion emitted a photon corresponding to a first line of the Lyman series. The photon liberateda photon electron from a stationary H atom in ground state. What is the velocity of photoelectron?

19. Alarm systems use the photoelectric effect. A beam of light strikes a piece of metal in the photocell, ejectingelectrons continuously and causing a small electric current to flow. When someone steps into the lightbeam, the current is interrupted and the alarm is triggered. What is the maximum wavelength of light thatcan be used in such an alarm system if the photocell metal is sodium, with a work function of 4.41 10-19J?

20. Use Bohr model to calculate the radius and energy of the B4+ ion in the n=3 state. How much energy wouldbe required to remove the electrons from 1 mol of B4+ in this state? What frequency and wavelength of lightwould be emitted in a transition from the n=3 to the n =2 state of this ion? Express all results in SI units.

21. The radiation emitted in the transition from the n=3 to the n =2 in a neutral hydrogen atom has a wavelength of 656.1 nm. What would be the wavelength of radiation emitted from a doubly ionized lithium atom (Li2+) if a transition occurred from the n=3 to the n =2? In what region of the spectrum does this radiation lie?

22. Both blue and green light eject electrons from the surface of potassium. In which case do the ejectedelectrons have the higher average kinetic energy?

23. Find the wavelengths of the first line of He+ ion spectral series whose4

1 2

interval between extreme lines is 1 1

2.7451= 10 cm 1

The radius of hydrogen atom in its ground state is 5.3 1011 m. After collision with an electron it is foundto have a radius of 21.2 1011m. The principal quantum number of the final state of the atom is

(a) 2 (b) 3 (c) 4 (d) 5

24.

25. Which element has a hydrogen like spectrum whose lines have wavelength one fourth of atomic hydrogen?

(a) He+ (b) Li2+ (c) Be3+ (d) B4+

26. Ionisation potential of hydrogen is 13.6 eV. Hydrogen atom in the ground state are excited

by monochromatic light of energy 12.1 eV. The spectral lines emitted by hydrogen according to Bohrs theory(a) One (b) Two (c) Three (d) Four

27. Column (I) Column (II)(a) Binding energy of He+ atom in an excited state (p) infrared region

(q) 3.4 eV(b) 7 3 transition in hydrogen atom

(c) 5 1 transition in hydrogen atom(d) Series limit of Balmer series in hydrogen atom

(r) 13.6 eV

(s) 10 spectral lines observed

28. Column I(a) Angular momentum

(b) Kinetic energy

(c) Potential energy

(d) Velocity

Column II(p) increases by increasing shell numbers

(q) decreases by decreasing atomic numbers

(r) increases by decreasing atomic numbers

(s) decreases by increasing shell numbers

Prime Classes for IIT-JEE/PMT, Ambedkar nagar UPS 2

29. Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy.a. n = 3 h n = 1 b. n = 2 h n = 4 c. n = 4 h n = 3

Find the longest wavelength of a wave that can travel around in a circular orbit of radius 1.8 m.30.