Question

What is the ratio of de Broglie wavelength of the particles if their kinetic energy are 0.002 eV and 2 eV respectively?

• A. 1:10
• B. 1:5
• C. 1:100
• D. 1:50

Hint:

For particles with different kinetic energies, the ratio of their de Broglie wavelengths is inversely proportional to the square root of the ratio of their kinetic energies.

Answer 1

The Correct Option is A

The de Broglie wavelength is given by the formula: \[ \lambda = \frac{h}{\sqrt{2mK}} \] where \( h \) is Planck’s constant, \( m \) is the mass of the particle, and \( K \) is the kinetic energy. Since the kinetic energy of the two particles are 0.002 eV and 2 eV, the ratio of their wavelengths is: \[ \frac{\lambda_1}{\lambda_2} = \sqrt{\frac{K_2}{K_1}} = \sqrt{\frac{2}{0.002}} = \sqrt{1000} = 31.62 \] Thus, the ratio of their wavelengths is approximately 1:10.