Question 1

Multiple choiceMedium1 mark

Two non-relativistic particles, X and Y, have masses mm and 2m2m and speeds vv and 3v3v respectively. Which row gives the momentum ratio pY/pXp_Y/p_X and de Broglie wavelength ratio λY/λX\lambda_Y/\lambda_X

Show answer and explanation

Answer: A. For non-relativistic particles, p=mvp=mv so pY/pX=(2m)(3v)/(mv)=6p_Y/p_X=(2m)(3v)/(mv)=6 Since λ=h/p\lambda=h/p λY/λX=pX/pY=1/6\lambda_Y/\lambda_X=p_X/p_Y=1/6

B: treats wavelength as directly proportional to momentum. C: omits the mass difference when comparing momenta, giving pY/pX=3p_Y/p_X=3 D: reverses the ratios, giving pX/pYp_X/p_Y and λX/λY\lambda_X/\lambda_Y instead.

Remember: de Broglie wavelength is inversely proportional to momentum.

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