• summary_type: revision
• word_count: 150

Quick reference for de Broglie wavelength calculations: General formula: λ = h/$\sqrt{2mKE}$ = h/$\sqrt{2mqV}$ for charged particles. Electron: λ = 12.27/√V Å. Proton: λ = 0.286/√V Å. Alpha: λ = 0.101/√V Å. Thermal: λ = h/$\sqrt{3mkT}$. Key ratios at same KE: λ_{1}/λ_{2} = $\sqrt{m_{2}/m_{1}}$. Same momentum: λ_{1} = λ_{2}. Same speed: λ_{1}/λ_{2} = m_{2}/m_{1}. Doubling KE: λ → λ/√2. Quadrupling KE: λ → λ/2. Doubling momentum: λ → λ/2. Bohr orbit connection: λ_n = 2πr_n/n = 2πna_{0}. JEE strategy: (1) Identify what's held constant (KE, p, or v). (2) Express λ in terms of that quantity. (3) Take the ratio. Most errors come from not identifying the correct constant or mixing up the formulas for same-KE and same-momentum cases.