IB Physics HL Theme E: Nuclear and quantum physics questions

Answer: C. The nuclear radius relation is $R=R_0A^{1/3}$ From the figure, $R_X/R_Y=(8/64)^{1/3}=1/2$ The mass ratio is $1/8$ and the spherical volume ratio is $(1/2)^3=1/8$ so $\rho_X/\rho_Y=(1/8)/(1/8)=1$

A: uses the mass ratio as the density ratio, omitting the volume comparison.
B: reverses the radius ratio, although its density ratio is unity.
D: treats the masses as equal and uses the inverse volume ratio, giving $8$
Remember: nuclear mass and volume both scale with nucleon number, so nuclear density is constant.

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

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

Remember: de Broglie wavelength is inversely proportional to momentum.

Answer: B. The energy released is the decrease in rest energy, $E_{\rm rel}=(M_i-M_f)c^2$ The initial rest energy is $E_i=M_i c^2$ so $\dfrac{E_{\rm rel}}{E_i}=\dfrac{(M_i-M_f)c^2}{M_i c^2}=\dfrac{M_i-M_f}{M_i}$

A: divides the mass defect by the final mass, not the initial mass.
C: gives the fraction of the initial rest energy that remains as product rest energy.
D: takes the reciprocal of the required fraction.
Remember: the energy released in fusion comes from the decrease in rest energy.