Chemistry : Quantum Mechanical Model of Atom

**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

*l *= 1 m* _{l} *= –1, 0, + 1

*l *= 2 m* _{l} *= –2, –1, 0, +1, +2

*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

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.**

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