Evaluate Yourself: 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 ⇒ 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 Fe³⁺ (z=26), Mn²⁺ (z=25) and argon (z=18)?

Solution:

Electronic configuration of Mn²⁺ is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s⁰ 3d⁵

Five unpaired electrons.

Electronic configuration of Ar: 1s² 2s² 2p⁶ 3s² 3p⁶

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? Ni²⁺ or Fe³⁺.

Solution:

Electronic configuration of Fe³⁺ : 1s² 2s² 2p⁶ 3s² 3p⁶ 4s⁰ 3d⁵

Electronic configuration of Ni²⁺ : 1s² 2s² 2p⁶ 3s² 3p⁶ 4s⁰ 3d⁸

Fe³⁺ has stable 3d⁵ half filled configuration.