The Nuclear Symbol

The nuclear symbol consists of three parts: the symbol of the element, the atomic number of the element and the mass number of the specific isotope.

Example #1: Here is a nuclear symbol:

${}_3^7\text{Li}$

The element symbol, Li, is that for lithium.

The three, subscripted left, is the atomic number and the seven, superscripted left, is the mass number.

Example #2: Here's another:

${}_{\mathrm{atomic\; number\; --->\; 2}}^{\mathrm{ mass\; number\; --->\; 4}}\text{He}$

The atomic number is:

the number of protons in the nucleus of the atom.

The mass number is:

the number of protons and neutrons in the nucleus of the atom.

The He is:

the symbol of the element helium.

Example #3: Here is one more example:

${}_{22}^{48}\text{Ti}$

The 22 is the atomic number for titanium and 48 is its mass number. The number of neutrons is 48 minus 22 = 26.

Example #4: Write the nuclear symbols for the three isotopes of oxygen that have mass numbers 16, 17, and 18. Then, determine the number of neutrons in each isotope.

Solution:

1) Nuclear symbols:

${}_{\mathrm{ 8}}^{16}\text{O}$

${}_{\mathrm{ 8}}^{17}\text{O}$

${}_{\mathrm{ 8}}^{18}\text{O}$

2) Number of neutrons:

O-16 ---> 16 − 8 = 8 neutrons
O-17 --- > 17 − 8 = 9 neutrons
O-18 ---> 18 − 8 = 10 neutrons

Example #5: True or False: atoms of Ca-41, K-41 and Ar-41 have the same number of neutrons. Explain your answer.

Solution:

The statement is false.

The 41 following the element symbol tells us the sum of the number of protons and number of neutrons. (It does not tell us the number of neutrons.)

The element symbol allows up to identify the number of protons in each element: Ca has 20, K has 19, and Ar has 18.

We can determine the number of electrons by subtracting the atomic number from the mass number, leaving us with 21 neutrons for Ca-41, 22 neutrons for K-41, and 23 neutrons for Ar-41.

Example #6: (a) Write the nuclear symbol for the chlorine isotope with 18 neutrons. (b) Write the nuclear symbol for the chlorine isotope having 20 neutrons. (c) Write the two nuclear symbols in "symbol-mass number" style.

Solution:

1) Important information to look up:

the symbol for chlorine ---> Cl.

the atomic number for chlorine ---> 17.

2) The answer to (a):

Add the atomic number (17) and the number of neutrons (18) to get the mass number of 35.

Write the nuclear symbol:

${}_{17}^{35}\text{Cl}$

3) The answer to (b):

Add the atomic number (17) and the number of neutrons (20) to get the mass number of 37.

Write the nuclear symbol:

${}_{17}^{37}\text{Cl}$

(c) "symbol-mass number" style:

Cl-35
Cl-37

The term "symbol-mass number" is not a standard term.

Example #7: How many electrons does the ion  ${}_{17}^{35}\text{Cl¯}$  have?

Solution:

This is a question that teachers like to surprise students with.

The answer starts with knowing that a neutral atom has the same number of electrons as protons. And, remember, the atomic number gives us the number of protons in the nucleus.

If there is a negative charge, then that means more electrons that protons. If the charge is positive, that means less electrons than protons.

A −1 charge means one more electron than protons. The answer is 18 electrons.

Example #8: How many electrons does the ion  ${}_{11}^{23}\text{Na⁺}$  have?

Solution:

The positive charge means the electrons are less in number than the protons.

A +1 charge means one less electron than the number of protons. The answer is 10 electrons.

Example #9: Two atoms are said to be nuclear mirrors when they have opposite numbers of protons and neutrons. What is the nuclear mirror of ${}_{\mathrm{ 8}}^{11}\text{O}$ ?

Solution:

The nuclear mirror would have 3 protons and 8 neutrons (the opposite of 8 protons and 3 neutrons for O-11).

The presence of 3 protons means lithium. Three protons and 8 neutrons means a mass number of 11.

${}_{\mathrm{ 3}}^{11}\text{Li}$

Example #10: What is the nuclear mirror for argon-32?

Solution:

Argon-32 has 18 protons and 14 neutrons.

Its mirror would have 14 protons and 18 neutrons.

Silicon-32.

Bonus Example: What is the mass number of an ion with 105 electrons, 159 neutrons, and a +1 charge?

Solution:

1) Neutrons:

The problem tells us explicitly that there are 159 neutrons.

2) Protons:

Electrons (negative) counterbalance protons (positive).

The +1 charge tells us there is one more proton than there are electrons.

Therefore, 106 protons.

2) Mass number:

159 + 106 = 265

The element is Erbium and the one whose first letter is deleted is Terbium. You may look up the atomic number.

Some comments:

1) The element name (or symbol) uniquely determines the atomic number. In the examples just above Ti is the only element with an atomic number of 22. So, if you need the atomic number, and all you know is the specific element, go to a periodic table and find its atomic number.

2) Suppose you are asked to write a nuclear symbol from scratch and the teacher requires it be a realistic one. Do this:

(a) Select an element, making sure it is a naturally occuring one. This will determine its atomic number.
(b) Take the element's atomic weight and round it off to the nearest whole number. More often than not, this will be the mass number of the most abundant stable isotope