The mass number of an isotope of an element is 298. If its nucleus has 196 neutrons, what is its atomic number?
Understanding Atomic Structure and Isotopes
The question asks us to find the atomic number of an isotope, given its mass number and the number of neutrons in its nucleus. This involves understanding the fundamental components of an atom's nucleus and how they relate to these numbers.
Let's define the key terms:
- Mass Number (A): The total number of protons and neutrons in the nucleus of an atom. It represents the approximate mass of the nucleus in atomic mass units.
- Atomic Number (Z): The number of protons in the nucleus of an atom. This number uniquely identifies an element. For a neutral atom, the atomic number is also equal to the number of electrons.
- Neutrons (N): Neutral particles found in the nucleus of an atom. Isotopes of an element have the same atomic number but different numbers of neutrons, leading to different mass numbers.
Relating Mass Number, Atomic Number, and Neutrons
The relationship between these three quantities is straightforward: the mass number is the sum of the number of protons (atomic number) and the number of neutrons. We can express this relationship with the following formula:
Mass Number (A) = Atomic Number (Z) + Number of Neutrons (N)
\$ A = Z + N \$
In this problem, we are given the mass number (A) and the number of neutrons (N), and we need to find the atomic number (Z). We can rearrange the formula to solve for Z:
Atomic Number (Z) = Mass Number (A) - Number of Neutrons (N)
\$ Z = A - N \$
Calculating the Atomic Number
We are given:
- Mass Number (A) = 298
- Number of Neutrons (N) = 196
Using the rearranged formula, we can calculate the atomic number (Z):
\$ Z = 298 - 196 \$
\$ Z = 102 \$
Therefore, the atomic number of the isotope is 102.
Checking the Options
Let's compare our calculated atomic number with the given options:
| Option | Value | Matches Calculation? |
|---|---|---|
| 1 | 196.0 | No |
| 2 | 298.0 | No |
| 3 | 102.0 | Yes |
| 4 | 494.0 | No |
Our calculated value of 102 matches Option 3. The number 196 is the number of neutrons, and 298 is the mass number. The sum of the mass number and neutrons (298 + 196 = 494) is not the atomic number.
Revision Table: Atomic Properties
| Property | Definition | Symbol | Used to Identify |
|---|---|---|---|
| Atomic Number | Number of protons | Z | Element |
| Mass Number | Number of protons + Number of neutrons | A | Specific isotope |
| Neutrons | Neutral particles in nucleus | N | Varies among isotopes of an element |
Additional Information: Isotopes Explained
Isotopes are atoms of the same element (same atomic number, Z) that have different numbers of neutrons (N). Because they have different numbers of neutrons, their mass numbers (A = Z + N) are also different. For example, Carbon-12 (\$ ^{12}C \$, 6 protons, 6 neutrons, A=12) and Carbon-14 (\$ ^{14}C \$, 6 protons, 8 neutrons, A=14) are isotopes of carbon. Both have an atomic number of 6, identifying them as carbon, but their different neutron counts give them different mass numbers. The isotope in this question, with an atomic number of 102, corresponds to the element Nobelium (No). An isotope with a mass number of 298 and 196 neutrons would be Nobelium-298 (\$ ^{298}No \$).
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