Question

Give the maximum number of orbitals in an atom that can have these quantum numbers:

n = 3                                                   _______________

n = 3, l = 1                                           ______________

n=2, l=1, m_l= 0                                    _______________

n=0, l=0, m_l=0                                     _______________

Removing the electron from a Hydrogen atom corresponds to a raising the electron from n=1 to an orbit that has n=∞.

           

What is the energy needed to remove the electron from a hydrogen atom?

What is the energy in terms of kJ per mole?

What is the maximum number of orbitals that are specified by each set of quantum numbers

n=3, l=2, m_l = -2

n=1, l=0

n=5

n=2, l=2

n=5, l=3

n = 2

Answer 1

1) What is the energy needed to remove the electron from a hydrogen atom?   What is the energy in terms of kJ per mole?

Energy in Joules:

   E = hc / λ   1/λ = R [ 1/n1^2- 1/n2^2]

Then,   E = hcR [ 1/n1^2- 1/n2^2]

   h = planck's constant = 6.626 x 10^-34 J.s

c = velocity of light = 3 x 10 ⁸ m/s

R = Rydberg constant = 1.097 x 10⁷ m^-1

n1=1, n2 = ∞

   E = hcR [ 1/n1^2- 1/n2^2]

= (6.626 x 10^-34 J.s) (3 x 10⁸ m/s) (1.097 x 10⁷ m^-1) [ 1/1^2- 1/∞^2]

= (6.626 x 10^-34 J.s) (3 x 10⁸ m/s) (1.097 x 10⁷ m^-1) [1-0]

= 21.8 x 10^-19 J

= 21.8 x 10^-22 kJ

E = 21.8 x 10^-22 kJ

Therefore, 21.8 x 10^-22 kJ  energy needed to remove the electron from a hydrogen atom.

Energy in kJ/mole

E = 21.8 x 10^-22 kJ

Multiply the energy with Avogadro number to get energy in kJ/mol.

E = 21.8 x 10^-22 J x Avogadro number

=  21.8 x 10^-22 J x 6.023 x 10²³ mol-1

= 1313 kJ/mole

E = 1313 kJ/mole

Therefore, energy needed to remove the electron from a hydrogen atom = 1313 kJ/mole

2) s - sublevel has 1 orbital

p - sublevel has 3 orbitals

d - sublevel has 5 orbitals

f - sublevel has 7 orbitals

g- sublevel has 9 orbitals

Give the maximum number of orbitals in an atom that can have these quantum numbers:

a) n = 3   

3s,3p,3d = 1 + 3 + 5 orbitals = 9 orbitals

b) n = 3, l = 1

3p = 3 orbitals

c) n=2, l=1, ml= 0

2pz orbital . So 1 orbital.

d) n=0, l=0, ml=0   

This set of quantum cannot exist bacause the value of ''n'' can never be zero.

So Zero orbitals.

3) What is the maximum number of orbitals that are specified by each set of quantum numbers

a) n=3, l=2, ml = -2

3d_x2-y2 orbital. So only1 orbital.

b) n=1, l=0

1s orbital . So So only1 orbital.

c) n=5

5s,5p,5d,5f, 5g = 1+ 3+ 5+ 7 + 9 orbitas = 25 orbitals

d) n=2, l=2

The value of l should always less than n.

Therefore,

these set of quantum numbers cannot exist.

So, Zero orbitals.

e) n=5, l=3

5f = 7 orbitals

f) n = 2

2s, 2p = 1 + 3 orbitals = 4 orbitals