Barium Atom Neutron Count Calculation

To find the number of neutrons in an atom, we need to understand the information provided by the atomic notation $ ^{A}_{Z}X $, where:

• 'X' is the chemical symbol of the element.
• 'Z' is the atomic number, which represents the number of protons in the nucleus.
• 'A' is the mass number, which represents the total number of protons and neutrons in the nucleus.

In this question, we are given the atom of Barium as $ ^{137}_{56}Ba $. Here:

• The atomic number (Z) is 56. This means a Barium atom has 56 protons.
• The mass number (A) is 137. This means the total number of protons and neutrons is 137.

Calculating Neutrons

The number of neutrons can be calculated using the formula:

Number of neutrons = Mass number (A) - Atomic number (Z)

Using LaTeX for the calculation:

$$ \text{Number of neutrons} = A - Z $$

Substituting the given values for Barium ($ ^{137}_{56}Ba $):

$$ \text{Number of neutrons} = 137 - 56 $$

$$ \text{Number of neutrons} = 81 $$

Therefore, the atom of Barium-137 ($ ^{137}_{56}Ba $) contains 81 neutrons.

Comparing this result with the given options:

• Option 1: 56 (Incorrect - represents protons)
• Option 2: 137 (Incorrect - represents mass number)
• Option 3: 193 (Incorrect calculation)
• Option 4: 81 (Correct - represents neutrons)

The correct option is 4.