The mass number of a nucleus is
(a) always less than its atomic number.
(b) always more than its ato

Q: Can the mass number ever be less than the atomic number?

No, because the mass number is the sum of protons and neutrons. Since the number of neutrons cannot be negative, the mass number must be at least equal to the atomic number.

Q: Are there any other elements besides Hydrogen where A = Z?

No. Protium ($^1_1\text{H}$) is the only known stable isotope in the universe where the nucleus contains no neutrons, making its mass number exactly equal to its atomic number.

Q: What is the difference between mass number and atomic mass?

Mass number is an integer representing the total number of nucleons (protons + neutrons). Atomic mass is the actual mass of the atom, usually expressed in atomic mass units (amu), and is typically a fractional value due to isotopes and mass defect.

Q: Why do heavier elements have more neutrons than protons?

As the number of protons increases, the electrostatic repulsion between them becomes very strong. More neutrons are needed to provide the attractive strong nuclear force to keep the nucleus stable.

Q: Does the mass number change during radioactive decay?

It depends on the type of decay. In alpha decay, the mass number decreases by 4. In beta and gamma decay, the mass number remains unchanged.

Question

The mass number of a nucleus is

Options:

(A) always less than its atomic number.

(B) always more than its atomic number.

(C) sometimes equal to its atomic number.

(D) sometimes more than and sometimes equal to its atomic number.

Sigma Percentile · Accepted Answer

### The Anatomy of a Nucleus

Imagine you are zooming into the heart of an atom, past the swirling clouds of electrons, right into the dense, compact core known as the nucleus. What do you see? You see a tightly packed cluster of particles: **protons** and **neutrons**. These particles are collectively called **nucleons**.

To describe this nucleus, physicists use two fundamental numbers. The first is the **atomic number**, denoted by $Z$. This is simply the count of protons. It is the identity badge of the element. If $Z=1$, you have Hydrogen. If $Z=6$, you have Carbon.

The second number is the **mass number**, denoted by $A$. This is the total count of all nucleons—both protons and neutrons. If we let $N$ represent the number of neutrons, we can write a very simple but powerful equation:

$$A = Z + N$$

### The Mathematical Constraint

Now, let's look at this equation logically. The number of neutrons, $N$, represents a physical count of particles. You can have zero neutrons, one neutron, or a hundred neutrons, but you can never have a *negative* number of neutrons.

Mathematically, this means $N \ge 0$.

If we substitute this logic back into our equation, we get a strict constraint:

$$A \ge Z$$

This tells us that the mass number $A$ will **always be greater than or equal to** the atomic number $Z$. It can never, ever be less. This immediately eliminates option (a) from our question.

### The Lone Exception: Protium

You might wonder, is the mass number *ever* exactly equal to the atomic number? For this to happen, $N$ must be exactly zero. Does such a nucleus exist?

Yes, it does! Look at the most abundant element in the universe: Hydrogen. Specifically, its most common isotope, **Protium** ($^1_1	ext{H}$). The nucleus of Protium consists of a single, lonely proton and absolutely zero neutrons.

For Protium:
$$Z = 1$$
$$N = 0$$
$$A = 1 + 0 = 1$$

Here, $A = Z$. This proves that the mass number is *sometimes equal* to the atomic number.

### The General Rule: Heavier Nuclei

What about literally every other isotope in the universe? Let's take another isotope of Hydrogen, called **Deuterium** ($^2_1	ext{H}$). This nucleus contains one proton and one neutron.

For Deuterium:
$$Z = 1$$
$$N = 1$$
$$A = 1 + 1 = 2$$

Here, $A > Z$. As we move to heavier elements, the number of neutrons not only equals the number of protons but eventually exceeds it to keep the nucleus stable against electrostatic repulsion. For example, Uranium-238 has 92 protons and 146 neutrons!

### The Final Verdict

By analyzing the physical reality of the nucleus, we have discovered that the mass number is sometimes exactly equal to the atomic number (as in the case of Protium) and sometimes strictly greater than the atomic number (as in Deuterium and all other heavier nuclei).

Therefore, both statements (c) and (d) perfectly describe the relationship between the mass number and the atomic number.

Animated Solution for Physics - Atoms and Nuclei: The mass number of a nucleus is

Select Answer:

Visualized Solution

$A = Z + N$

$N \geq 0 ⟹ A \geq Z$

$Case 1: A = Z$

$Case 2: A > Z$

$Conclusion$

The Sigma Insight: Nucleus and Nuclear Reaction

The Anatomy of a Nucleus

The Mathematical Constraint

The Lone Exception

The General Rule

The Final Verdict

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