1. Calculate the de-Broglie wavelength of an electron that has been accelerated from rest through a potential difference of 1 keV.
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.
3. How many orbitals are possible in the 4th energy level? (n=4)
n = 4
l = 0, 1, 2, 3
∴ 4 sub shells s, p, d & f.
l = 0 ml = 0 ⇒ one 4s orbital.
l = 1 ml = –1, 0, + 1 ⇒ three 4p orbitals.
l = 2 ml = –2, –1, 0, +1, +2 ⇒ five 4d orbitals.
l = 3 ml = –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
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?
6. How many unpaired electrons are present in the ground state of Fe3+ (z=26), Mn2+ (z=25) and argon (z=18)?
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 4f2. Write all the four quantum numbers for these electrons.
n = 4 ; f orbital l = 3 ⇒ ml = – 3, –2, –1, 0, +1, +2
Out of two electrons, one electron occupies 4f orbital with ml = –3 and another electron occupies 4f orbital with ml = –2.
All the four quantum numbers for the two electrons are
8. Which has the stable electronic configuration? Ni2+ or Fe3+.
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.