Question

Determine ratio of de broglie wavelength of \(α- particle\) and proton of same kinetic energy is

Answer 1

The correct answer is: 1:2. The relationship between wavelength (λ), Planck's constant (h), mass (m), and kinetic energy (E_k) is given by \(λ=\frac{h}{\sqrt2mE_k}\). The ratio of the wavelength of an alpha particle (\(λ_α\)) to the wavelength of a proton (\(λ_p\)) is equal to the square root of the inverse ratio of their masses: \(\frac{λ_α}{λ_p}=\sqrt{\frac{m_p}{m_α}}\), which simplifies to \(\sqrt{\frac{1}{4}}=\frac{1}{2}\).