Q. 9 - An Introduction to General, Organic, and Biological Chemistry

Question

The naturally occurring isotopes of silicon are listed in the following table: ($4.5, 4.6, 5.2, 5.4, 6.6, 6.7$)

a. Complete the table with the number of protons, neutrons, and electrons for each isotope listed:

b. What is the electron arrangement of silicon? 

c. Which isotope is the most abundant, if the atomic mass for Silicon is $28.09$?

d. Write the balanced nuclear equation for the beta decay of the radioactive isotope $\mathrm{Si}-31$.

e. Draw the Lewis structure and predict the shape of ${\mathrm{SiCl}}_4$ 

f. How many hours are needed for a sample of $Si-31$ with an activity of $16 \mu Ci$ to decay to $2.0 \mu Ci$?

Step-by-Step Solution

Answer

(a) The required table is given below:

Isotope	Number of protons	Number of neutrons	Number of electrons
${}_{14}{}^{28}\mathrm{Si}$	$14$	$14$	$14$
${}_{14}{}^{29}\mathrm{Si}$	$14$	$15$	$14$
${}_{14}{}^{30}\mathrm{Si}$	$14$	$16$	$14$

(b) Electron arrangement of silicon is $2, 8, 4$

(c) Isotope which is most abundant is ${}_{14}{}^{28}\mathrm{Si}$

(d) The balanced equation is ${}_{14}{}^{31}\mathrm{Si}\to {}_{15}{}^{31}\mathrm{P}+{}_{-1}{}^0\mathrm{\beta }$

(e) The required Lewis structure and shape is given below

(f) The time needed is  $4 h$

Part (a) Step 1: Given information

We need to complete the given table

Part (a) Step 1: Explanation

We know that

Atomic no. is equal to no. of protons or no. of electrons

And mass no. is equal to sum of no. of neutrons and no. of protons

So, The required table is,

Isotope	Number of protons	Number of neutrons	Number of electrons
${}_{14}{}^{28}\mathrm{Si}$	$14$	$14$	$14$
${}_{14}{}^{29}\mathrm{Si}$	$14$	$15$	$14$
${}_{14}{}^{30}\mathrm{Si}$	$14$	$16$	$14$

Part (b) Step 1: Given information

We need to find the electron arrangement of silicon 

Part (b) Step 2: Explanation

From part (a)

We know that

No. of electrons are $14$

Therefore, the electron arrangement of silicon is,

$2, 8, 4$

Part (c) Step 1: Given information

We need to find the most abundant isotope of silicon

Part (c) Step 2: Explanation

We know that

The atomic mass of silicon is, $28.09$ which is not the actual mass but the average masses of different isotopes.

As this mass is closest to the isotope $Si-28$

Therefore, most abundant isotope is, 

${}_{14}{}^{28}\mathrm{Si}$

Part (d) Step 1: Given information

We need to find the balanced nuclear equation for the beta decay of the radioactive isotope 

Part (d) Step 2: Explanation

We know that

Element goes under $\beta -$decay

So the $\beta$ atom will be one of the product

Therefore, the balanced nuclear equation for the beta decay of the radioactive isotope is

${}_{14}{}^{31}\mathrm{Si}\to {}_{15}{}^{31}\mathrm{P}+{}_{-1}{}^0\mathrm{\beta }$

Part (e) Step 1: Given information

We need to draw the lewis structure and determine the shape of ${\mathrm{SiCl}}_4$

Part (e) Step 2: Explanation

We know that, 

$\mathrm{Cl}$ belongs to group seven, meaning it possesses seven valence electrons.

$\mathrm{Si}$ belongs to group four, meaning it possesses four valence electrons.

As a result, the molecule has a total of $32$ valence electrons.

$\mathrm{Si}$ is the center atom because there is only one $\mathrm{Si}$ in the molecule.

As a result, the molecule's Lewis structure is:

Now, according to VSEPR theory the shape of ${\mathrm{SiCl}}_4$ is tetrahedral.

Part (e) Step 1: Given information

We need to find the time of the activity

Part (e) Step 2: Explanation

We know that

• The Activity of sample is, $16 \mathrm{\mu Ci}$
• Activity after decay is, $2.0 \mu Ci$

So, The time required for the decaying of sample is, $4 h$