Key relationship
rn=a₀n²/Z; En=−13.606Z²/n² eV; vn=Zv₁/n.
Physics · Class 12
Hydrogen-like ions
A stronger nuclear charge attracts the same single electron more tightly. At fixed n, radius decreases as1/Z and binding energy magnitude increases as Z². Hydrogen-like means one electron, including charged ions.
Open the interactive experiment →Hydrogen-like ions
ஒரே எலக்ட்ரான் உள்ள அயன்களில் Z அதிகரித்தால் ஆரம் குறையும்; பிணைப்பு ஆற்றல் Z² விகிதத்தில் அதிகரிக்கும்.
Key notes, relationships and model limits
Remember
A stronger nuclear charge attracts the same single electron more tightly. At fixed n, radius decreases as1/Z and binding energy magnitude increases as Z². Hydrogen-like means one electron, including charged ions.
Common trap
Neutral helium has two electrons and is outside this simple hydrogen-like model.
Model limits
Exactly one bound electron; nonrelativistic low-Z Bohr approximation. This is not a many-electron atom model.
What you will learn
Apply one-electron scaling to ions.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
He⁺ at n1 has r≈0.02646 nm and E≈−54.423 eV.
Why this matters
The model connects hydrogen-like ions with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
At fixed n, doubling Z changes binding-energy magnitude by?
- Two
- Four
- Half
Read the explanation
Energy magnitude scales as Z².
Course connection: Class XII Chapter 12. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.