Evaluate Yourself
1. Calculate the de-Broglie
wavelength of an electron that has been accelerated from rest through a
potential difference of 1 keV.
Solution:
Given: accelerated potential = 1 keV
The kinetic energy of the electron = the energy due
to accelerating potential.
m = mass of the electron = 9.1 × 10^{–31}
kg
h = Planck constant = 6.626 × 10^{–34} Js 1
1eV = 1.6 × 10^{–19} J
2. Calculate the uncertainty in
the position of an electron, if the uncertainty in its velocity is 5.7 × 105
ms-1.
Solution:
3. How many orbitals are possible
in the 4th energy level? (n=4)
Solution:
n = 4
l = 0, 1,
2, 3
∴ 4 sub
shells s, p, d & f.
l = 0 m_{l} = 0 ⇒ one 4s orbital.
l = 1 m_{l} = –1, 0, + 1 ⇒ three 4p
orbitals.
l = 2 m_{l} = –2, –1, 0, +1, +2 ⇒ five 4d
orbitals.
l = 3 m_{l} = –3, –2, –1, 0, +1, +2, +3⇒
seven 4f orbitals.
Over all 16 orbitals are possible.
4. Calculate the total number of
angular nodes and radial nodes present in 3d and 4f orbitals
Solution:
5. Energy of an electron in
hydrogen atom in ground state is -13.6 eV. What is the energy of the electron
in the second excited state?
Solution:
6. How many unpaired electrons are
present in the ground state of Fe^{3+} (z=26), Mn^{2+} (z=25)
and argon (z=18)?
Solution:
Electronic configuration of Mn^{2+} is 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{0} 3d^{5}
Five
unpaired electrons.
Electronic configuration of Ar: 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}
no
unpaired electrons.
7. Explain the meaning of the
symbol 4f^{2.} Write all the four quantum numbers for these electrons.
Solution:
n = 4 ; f orbital l = 3 ⇒ m_{l} = – 3, –2, –1, 0, +1, +2
Out of two electrons, one electron occupies 4f
orbital with m_{l} = –3 and
another electron occupies 4f orbital with m_{l}
= –2.
All the four quantum numbers for the two electrons
are
8. Which has the stable electronic
configuration? Ni^{2+} or Fe^{3+}.
Solution:
Electronic configuration of Fe^{3+} : 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{0} 3d^{5}
Electronic configuration of Ni^{2+} : 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{0} 3d^{8}
Fe^{3+}
has stable 3d^{5} half filled configuration.