Question

Proton and electron have equal kinetic energy, the ratio of de-Broglie wavelength of proton and electron is \(\frac{1}{x}\). Find x. (Mass of proton 1849 times mass of electron)

Answer 1

Given:
Kinetic energy of proton = kinetic energy of electron
Mass of proton = 1849 × mass of electron

Step 1: de-Broglie wavelength formula
λ = h / √(2mK)

Step 2: Since kinetic energy is same
λ ∝ 1 / √m

Step 3: Ratio of wavelengths
\[ \frac{\lambda_p}{\lambda_e} = \sqrt{\frac{m_e}{m_p}} \]

Step 4: Substitute values
\[ \frac{\lambda_p}{\lambda_e} = \sqrt{\frac{1}{1849}} = \frac{1}{43} \]

Final Answer: 1/43