Question

homework set #10
please print and show all work and answers on a separate paper.

1. how does de broglies hypothesis account for the fact that the energies of the electron in a hydrogen atom are quantized?
2. describe the shapes of the s and p orbitals. how are these orbitals related to the quantum numbers n, l, and m_l?
3. give the values of the four quantum numbers of an electron in the following orbitals: (a) 3s, (b) 4p, (c) 3d.
4. indicate which of the following sets of quantum numbers are unacceptable and explain why: (a) (1, 0, +1/2, +1/2) (b) (3, 0, 0, +1/2) (c) (2, 2, 1, +1/2) (d) (4, 3, -2, +1/2) (e) (3, 2, 1, 1)
5. write the ground - state electronic configurations for the following elements: ge, fe, zn, ti.
6. draw the lewis structure and give the molecular shape description of the following: pcl_5, nh_3, co_3^2-, c_2h_4, xef_4.
7. determine the formal charge of each element in the following: h_3o^+, nh_3.

Explanation:

1. De Broglie's hypothesis posits that electrons have wave - like properties. In a hydrogen atom, for an electron's orbit to be stable, the circumference of the orbit must be an integral multiple of the de - Broglie wavelength ($2\pi r = n\lambda$). This leads to quantized angular momentum ($L = mvr=\frac{nh}{2\pi}$) and thus quantized energies.
2. The s - orbital is spherical in shape. The p - orbital has a dumb - bell shape. The principal quantum number $n$ determines the energy level and size of the orbital. The angular momentum quantum number $l$ determines the shape of the orbital ($l = 0$ for s, $l = 1$ for p). The magnetic quantum number $m_l$ determines the orientation of the orbital in space.

3.

• For 3s: $n = 3$, $l=0$, $m_l = 0$, $m_s=\pm\frac{1}{2}$
• For 4p: $n = 4$, $l = 1$, $m_l=- 1,0,1$, $m_s=\pm\frac{1}{2}$
• For 3d: $n = 3$, $l = 2$, $m_l=-2,-1,0,1,2$, $m_s=\pm\frac{1}{2}$

4.

• (a) Unacceptable because an electron cannot have the same spin quantum number value twice in the same set of quantum numbers for a single - electron description.
• (b) Acceptable.
• (c) Unacceptable as for $n = 2$, $l$ can only be 0 or 1, not 2.
• (d) Acceptable.
• (e) Unacceptable as the spin quantum number $m_s$ can only be $\pm\frac{1}{2}$, not 1.

5.

• Ge: $1s^22s^22p^63s^23p^64s^23d^{10}4p^2$
• Fe: $1s^22s^22p^63s^23p^64s^23d^6$
• Zn: $1s^22s^22p^63s^23p^64s^23d^{10}$
• Ti: $1s^22s^22p^63s^23p^64s^23d^2$

6.

• $PCl_5$: Lewis structure has P in the center with 5 Cl atoms around it. Molecular shape is trigonal bipyramidal.
• $NH_3$: Lewis structure has N in the center with 3 H atoms and a lone pair. Molecular shape is trigonal pyramidal.
• $CO_3^{2 - }$: Lewis structure has C in the center with 3 O atoms, resonance structures exist. Molecular shape is trigonal planar.
• $C_2H_4$: Lewis structure has a double - bond between the two C atoms and H atoms attached to C. Molecular shape is planar.
• $XeF_4$: Lewis structure has Xe in the center with 4 F atoms and 2 lone pairs. Molecular shape is square planar.

7.

• For $H_3O^+$:
• O: Formal charge=$6-(2 + \frac{6}{2})=1$
• H: Formal charge=$1 - 1=0$
• For $NH_3$:
• N: Formal charge=$5-(2+\frac{6}{2}) = 0$
• H: Formal charge=$1 - 1=0$

Answer:

1. De Broglie's hypothesis links electron's wave - like nature to quantized orbits and energies in hydrogen atom.
2. s - spherical, p - dumb - bell; $n$ for energy/size, $l$ for shape, $m_l$ for orientation.
3. 3s: $n = 3$, $l=0$, $m_l = 0$, $m_s=\pm\frac{1}{2}$; 4p: $n = 4$, $l = 1$, $m_l=- 1,0,1$, $m_s=\pm\frac{1}{2}$; 3d: $n = 3$, $l = 2$, $m_l=-2,-1,0,1,2$, $m_s=\pm\frac{1}{2}$
4. (a) Unacceptable; (b) Acceptable; (c) Unacceptable; (d) Acceptable; (e) Unacceptable
5. Ge: $1s^22s^22p^63s^23p^64s^23d^{10}4p^2$; Fe: $1s^22s^22p^63s^23p^64s^23d^6$; Zn: $1s^22s^22p^63s^23p^64s^23d^{10}$; Ti: $1s^22s^22p^63s^23p^64s^23d^2$
6. $PCl_5$: trigonal bipyramidal; $NH_3$: trigonal pyramidal; $CO_3^{2 - }$: trigonal planar; $C_2H_4$: planar; $XeF_4$: square planar
7. $H_3O^+$: O: 1, H: 0; $NH_3$: N: 0, H: 0