Q.1. The angular momentum of an electron in a Bohr's orbit of hydrogen atom is 4.218 × 10−34 kg m2 s−1. Calculate the wavelength of the spectral line emitted when electron falls from this level to next lower level.
Ans: 1.876 × 10−4 cm
Q.2. Calculate the ratio of wavelength of first spectral line of Lyman and Balmer series of hydrogen spectrum.
Ans: 5 : 27
Q.3. Find out the number of waves made by a Bohr electron in one complete revolution in its 3rd orbit.
Ans: 3
Q.4. An electron in a H-atom in its ground state absorbs 1.50 times as much energy as the minimum energy required for it to escape from the atom. What is the wavelength of the emitted electron?
Ans: 4.70 × 10−10 m
Q.5. Which of the following sets of orbitals are degenerate and why?
(i) 1s, 2s, and 3s in Mg atom
(ii) 2px, 2py and 2pz in C atom
(iii) 3s, 3px and 3d orbitals in H atom.
Ans: No, Yes, Yes
Q.6. What is the difference in the orbital angular momentum of 2p and 3p electron ? Explain.
Ans: No difference.
Q.7. Predict the number of nodes and nodal planes in
(i) 3px
(ii) 4s
(iii) 3dx2 − y2 orbital.
Ans: (i) 1, 1 (ii) 3, 0 (iii) 0, 2
Q.8. For H atom the Bohr radius for first orbit is 0.529 Å and the radius of maximum probability for H-atom according to wave mechanical model is also 0.529 Å How do the two approaches differ ?
Q.9. For a multielectron atom, the maximum of 2p-orbital in radial probability distribution graph is nearer the nucleus than that of 2s-orbital. Therefore 2p-orbital should be closer to the nucleus and lower in energy than 2s-orbital. But 2s-orbital has lower energy than 2p-orbital. Explain.
Q.10. Calculate the velocity (cm s−1) of an electron placed in third orbit of the hydrogen atom. Also calculate the number of revolutions per second that this electron makes around the nucleus.
Ans: (i) 7.27 × 107 cm s−1 (ii) 2.42 × 1014
Q.11. Which state of the triple ionized beryllium (Be3+) has the same orbit radius as that of the ground state of hydrogen atom?
Ans: n = 2
Q.12. The angular momentum of an electron in Bohr's orbit of H-atom is 3.02 × l0−34 kg m2 s−1. Calculate the wavelength of the spectral line emitted when the electron jumps from this level to the next lower level.
Ans: 656 nm.
Q.13. An electron in certain Bohr orbit has velocity 1/275 of the velocity of light. Calculate the orbit in which the electron is revolving.
Ans: n = 2
Q.14. Write time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom in terms of mass m, radius r, orbit n and plank’s constant h.
Ans: (4π2mr2)/nh