Subatomic Particles & Isotopes

Theory Exercises

Subatomic Particles & Atomic Calculations

The Three Subatomic Particles

Particle	Symbol	Charge	Mass (u)	Mass (kg)	Location
Proton	p	+1	1	1.673 × 10⁻²⁷	Nucleus
Neutron	n	0	1	1.675 × 10⁻²⁷	Nucleus
Electron	e	-1	≈ 0	9.109 × 10⁻³¹	Electron cloud

Key Formulas

Symbol	Name	Formula
Z	Atomic number	= number of protons
A	Mass number	= protons + neutrons
n	Neutrons	= A - Z
e	Electrons (neutral)	= protons
Charge	Ion charge	= protons - electrons

Worked Examples

Example 1: Neutral Atom — ¹⁶₈O (Oxygen-16)

Symbol	Value	How?
Z	8	Given (bottom number)
A	16	Given (top number)
p	8	p = Z
n	8	n = A - Z = 16 - 8
e	8	e = p (neutral)
Charge	0	Neutral atom

Example 2: Cation (+) — ²³₁₁Na⁺ (Sodium ion)

Symbol	Value	How?
Z	11	Given
A	23	Given
p	11	p = Z
n	12	n = A - Z = 23 - 11
e	10	Lost 1 electron
Charge	+1	p - e = 11 - 10

Example 3: Anion (-) — ³²₁₆S²⁻ (Sulfide ion)

Symbol	Value	How?
Z	16	Given
A	32	Given
p	16	p = Z
n	16	n = A - Z = 32 - 16
e	18	Gained 2 electrons
Charge	-2	p - e = 16 - 18

Example 4: Identify from particles — p = 26, n = 30, e = 24

Symbol	Value	How?
p	26	Given
Z	26	Z = p
Element	Iron (Fe)	Look up Z = 26
n	30	Given
A	56	A = p + n = 26 + 30
e	24	Given
Charge	+2	p - e = 26 - 24
Ion	Fe²⁺	Cation (lost 2 e)

Practice Tables

Table 1: Neutral Atoms

Complete the missing values:

Element	Symbol	Z	A	p	n	e
Hydrogen	¹₁H	1	1	1	0	1
Carbon	¹²₆C	6	12	6	6	6
Nitrogen	¹⁴₇N	7	14	7	7	7
Oxygen	¹⁶₈O	8	16	8	8	8
Sodium	²³₁₁Na	11	23	11	12	11
Chlorine	³⁵₁₇Cl	17	35	17	18	17
Iron	⁵⁶₂₆Fe	26	56	26	30	26

Table 2: Cations (Positive Ions)

Ion	Z	A	p	n	e	Charge
Na⁺	11	23	11	12	10	+1
K⁺	19	39	19	20	18	+1
Mg²⁺	12	24	12	12	10	+2
Ca²⁺	20	40	20	20	18	+2
Al³⁺	13	27	13	14	10	+3
Fe²⁺	26	56	26	30	24	+2
Fe³⁺	26	56	26	30	23	+3
Cu²⁺	29	64	29	35	27	+2

Table 3: Anions (Negative Ions)

Ion	Z	A	p	n	e	Charge
F⁻	9	19	9	10	10	-1
Cl⁻	17	35	17	18	18	-1
Br⁻	35	80	35	45	36	-1
O²⁻	8	16	8	8	10	-2
S²⁻	16	32	16	16	18	-2
N³⁻	7	14	7	7	10	-3
P³⁻	15	31	15	16	18	-3

Isotopes

Isotopes = Same Z (protons), different n (neutrons)

Hydrogen Isotopes

Name	Symbol	Z	A	p	n	e	Abundance	Stability	Use / Occurrence
Protium	¹₁H	1	1	1	0	1	99.98%	Stable	Most common; found in water (H₂O) and organic compounds
Deuterium	²₁H (D)	1	2	1	1	1	0.02%	Stable	Heavy water (D₂O) in nuclear reactors; NMR spectroscopy
Tritium	³₁H (T)	1	3	1	2	1	Trace	☢️ Radioactive (t½ = 12.3 y)	Nuclear fusion fuel; glow-in-the-dark watches; produced in nuclear reactors

Carbon Isotopes

Name	Symbol	Z	A	p	n	e	Abundance	Stability	Use / Occurrence
Carbon-12	¹²₆C	6	12	6	6	6	98.9%	Stable	Standard for atomic mass unit (1 u = 1/12 of ¹²C); all organic matter
Carbon-13	¹³₆C	6	13	6	7	6	1.1%	Stable	NMR spectroscopy; metabolic studies; climate research
Carbon-14	¹⁴₆C	6	14	6	8	6	Trace	☢️ Radioactive (t½ = 5,730 y)	Radiocarbon dating of fossils and archaeological artifacts; formed in atmosphere by cosmic rays

Nuclear Stability Chart

Identify the Element

Use the periodic table to identify elements from their data:

Table 4: Find the Element

Z	A	p	n	e	Charge	Element	Isotope	Symbol
1	1	1	0	1	0	Hydrogen	Protium	¹H
6	12	6	6	6	0	Carbon	Carbon-12	¹²C
8	16	8	8	10	-2	Oxygen	Oxygen-16	¹⁶O^2-
11	23	11	12	10	+1	Sodium	Sodium-23	²³Na⁺
17	35	17	18	18	-1	Chlorine	Chlorine-35	³⁵Cl^-
26	56	26	30	24	+2	Iron	Iron-56	⁵⁶Fe²⁺
20	40	20	20	18	+2	Calcium	Calcium-40	⁴⁰Ca²⁺

Quick Reference

To find...	Formula
Z	= p (protons)
A	= p + n
p	= Z
n	= A - Z
e (neutral)	= p
e (ion)	= p - charge
Charge	= p - e

Ion Rules

Cation (+): e < p (lost electrons)
Anion (-): e > p (gained electrons)
Neutral: e = p