Chlorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. This indicates the ratio o

NCERT Exemplar · Q13

Q. Chlorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. This indicates the ratio of Cl-37 and Cl-35 is approximately

(i) 1:2

(ii) 1:1

(iii) 1:3

(iv) 3:1

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Concept understanding — Atomic Notation

Atomic Notation: The ID Card of an Atom

Imagine you're at a huge stadium filled with people. To identify any one person, you'd need more than just a name — you'd need their jersey number, their team, maybe their position. An atom is the same way. Just saying "carbon" or "oxygen" tells you the kind of atom, but not the full story. Atomic notation is the shorthand that gives you the complete identity.

The Intuition: Three Numbers, One Symbol

Every atom is built from three key particles:

Protons (positive charge) — these define what element it is.
Neutrons (no charge) — these add mass and stability.
Electrons (negative charge) — these orbit the nucleus and determine chemical behaviour.

Atomic notation packs all this information around the element's symbol. Think of it as a label with two numbers attached:

^{A}_{Z}\text{X}

Where:

X is the element symbol (e.g., C for carbon, O for oxygen).
Z is the atomic number (number of protons).
A is the mass number (protons + neutrons).

Note

The atomic number $Z$ is what makes an atom that element. Change $Z$ , and you change the element entirely. Carbon always has $Z=6$ ; if you change it to $7$ , it's nitrogen.

The Precise Statement

For any atom represented as $^{A}_{Z}\text{X}$ :

Atomic number $Z$ = number of protons = number of electrons (in a neutral atom).
Mass number $A$ = number of protons + number of neutrons.
Number of neutrons $N = A - Z$ .

A neutral atom has equal protons and electrons. If the atom gains or loses electrons, it becomes an ion — but the notation for the nucleus stays the same.

Example: Carbon-12

The most common carbon atom is written as:

^{12}_{6}\text{C}

From this:

$Z=6$ → 6 protons, and in a neutral atom, 6 electrons.
$A=12$ → total nucleons (protons + neutrons) = 12.
Neutrons $N = 12 - 6 = 6$ .

Why Two Numbers? Why Not Just One?

If you only knew the mass number $A$ , you wouldn't know the element — because different elements can have the same mass number (e.g., $^{14}\text{C}$ and $^{14}\text{N}$ both have $A=14$ ). If you only knew the atomic number $Z$ , you wouldn't know how many neutrons are present — and that matters for isotopes.

Important

Isotopes are atoms of the same element (same $Z$ ) with different numbers of neutrons (different $A$ ). For example:

$^{12}_{6}\text{C}$ (6 neutrons)
$^{13}_{6}\text{C}$ (7 neutrons)
$^{14}_{6}\text{C}$ (8 neutrons) All are carbon, but they have different masses and some are radioactive.

A Quick Table for Clarity

Notation	Element	Protons ( $Z$ )	Neutrons ( $N$ )	Mass Number ( $A$ )
$^{1}_{1}\text{H}$	Hydrogen	1	0	1
$^{4}_{2}\text{He}$	Helium	2	2	4
$^{23}_{11}\text{Na}$	Sodium	11	12	23

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The average atomic mass of an element is the weighted average of the masses of its isotopes. By setting up an equation using the given average atomic mass and the masses of the two chlorine isotopes, we find that the ratio of Cl-37 to Cl-35 is approximately $\boxed{1:3}$ .

When we talk about the atomic mass of an element, like the 35.5 for chlorine, we are usually referring to its average atomic mass. This is because most elements naturally exist as a mixture of different isotopes. Isotopes of an element have the same number of protons (and thus the same atomic number) but different numbers of neutrons, leading to different mass numbers.

The average atomic mass is a weighted average of the masses of all naturally occurring isotopes of an element, with the weighting factor being the fractional abundance of each isotope. This concept is crucial for understanding why the atomic mass on the periodic table is rarely a whole number.

\text{Average Atomic Mass} = \sum (\text{mass of isotope}_i \times \text{fractional abundance of isotope}_i)

Let's apply this concept to chlorine.

Identify the given information:
- Chlorine has two isotopes: Cl-37 and Cl-35. This means their approximate mass numbers are 37 and 35 atomic mass units (amu), respectively.
- The average atomic mass of chlorine is given as 35.5 amu.
Define variables for isotopic abundance:

Let $p_{35}$ be the fractional abundance of Cl-35.

Let $p_{37}$ be the fractional abundance of Cl-37.

Since these are the only two isotopes, their fractional abundances must sum to 1 (or 100%).

Therefore, $p_{35} + p_{37} = 1$ .

This implies $p_{37} = 1 - p_{35}$ .
Set up the equation for average atomic mass:

Using the formula for average atomic mass:

\text{Average Atomic Mass} = (\text{mass of Cl-35} \times p_{35}) + (\text{mass of Cl-37} \times p_{37})

Substitute the known values:

35.5 = (35 \times p_{35}) + (37 \times p_{37})

Solve the equation for the abundances: Substitute $p_{37} = 1 - p_{35}$ into the equation:

35.5 = (35 \times p_{35}) + (37 \times (1 - p_{35}))

Expand the equation: …

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Q.Chlorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. This indicates the ratio of Cl-37 and Cl-35 is approximately

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