Interactive Calculation Tools

🧠 Why Use These Calculators?

These aren't just for getting answers. Use them to:

Verify your manual calculations
Understand how parameters affect results
Develop intuition for typical value ranges

In exam, you still calculate manually. These build your intuition.

1. Photoelectric Effect Calculator

Calculate kinetic energy and stopping potential for photoelectric effect.

Frequency (Hz):

Work Function (eV):

🎯 Try These

Test 1: ν = 6 × 10¹⁴ Hz, φ = 2.0 eV (Sodium)
Test 2: ν = 1 × 10¹⁵ Hz, φ = 4.3 eV (Zinc)
Test 3: ν = 5 × 10¹⁴ Hz, φ = 2.14 eV (Cesium)

Observe when photoelectric effect occurs and when it doesn't!

2. de Broglie Wavelength Calculator

Calculate matter wave wavelength for any particle.

Mass (kg):

Velocity (m/s):

🔬 Exam Insight

Typical wavelength ranges:

Electron (100V): λ ≈ 1.2 Å (X-ray range)
Proton (100V): λ ≈ 0.03 Å
Cricket ball: λ ≈ 10⁻³⁴ m (unobservable)

If exam asks "Is wave nature observable?", compare λ to object size.

3. Photon Energy Calculator

Convert between wavelength, frequency, and energy.

Wavelength (nm):

❌ Common Mistake Alert

Students forget unit conversions:

Wavelength in nm → convert to m (multiply by 10⁻⁹)
Result in J → convert to eV (divide by 1.6 × 10⁻¹⁹)

Or use hc = 1240 eV·nm directly. Much faster.

Quick Reference Tables

Standard Work Functions

Metal	φ (eV)	λ₀ (nm)
Cesium	2.14	580
Potassium	2.30	540
Sodium	2.75	450
Calcium	3.20	388
Zinc	4.30	288
Silver	4.70	264

Electromagnetic Spectrum

Region	Wavelength	Energy (eV)
Gamma	< 0.01 nm	> 100 keV
X-ray	0.01-10 nm	100 eV-100 keV
UV	10-400 nm	3-100 eV
Visible	400-700 nm	1.8-3.1 eV
IR	700 nm-1 mm	0.001-1.8 eV

Worked Examples Using Calculators

Example 1: Photoelectric Effect

Problem: Light of wavelength 300 nm falls on sodium (φ = 2.75 eV). Find maximum KE and stopping potential.

Step 1: Convert wavelength to frequency

ν = c/λ = (3 × 10⁸)/(300 × 10⁻⁹) = 1 × 10¹⁵ Hz

Step 2: Use calculator above

Enter: ν = 1 × 10¹⁵ Hz, φ = 2.75 eV

Step 3: Verify manually

E_photon = hν = (4.14 × 10⁻¹⁵)(1 × 10¹⁵) = 4.14 eV
KE_max = 4.14 - 2.75 = 1.39 eV
V₀ = 1.39 V

Example 2: de Broglie Wavelength

Problem: Electron accelerated through 100V. Find its de Broglie wavelength.

Method 1: Formula

λ = 12.27/√V = 12.27/√100 = 1.227 Å

Method 2: Find velocity first

eV = (1/2)mv²
v = √(2eV/m) = √(2 × 1.6 × 10⁻¹⁹ × 100 / 9.1 × 10⁻³¹)
v ≈ 5.93 × 10⁶ m/s

Use calculator: m = 9.1 × 10⁻³¹ kg, v = 5.93 × 10⁶ m/s

Result: λ ≈ 1.23 × 10⁻¹⁰ m = 1.23 Å ✓

Practiced with Calculators?

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