20A_Midterm2

19F-CHEM20A-1 Exam 2 ELLA HIRATA TOTAL POINTS 78 / 100 QUESTION 1 1 30 pts 1.1 1a 8 / 8 ✓ + 8 pts Correct, 13.6 eV + 6 pts -13.6 eV + 4 pts 122 eV + 3 pts -122 eV + 2 pts $$ E_n = -\frac {Z^2}{n^2}R$$ - 2 pts Math or unit error or incorrect answer or no work shown 1.2 1b 8 / 8 ✓ + 8 pts Correct, $$\psi_{100}$$, $$\psi_{200}$$, $$\psi_{210}$$, $$\psi_{211}$$,$$\psi_{21-1}$$, $$\psi_{300}$$ + 4 pts At least 2 of the right wavefunctions + 1 pts 1 correct wavefunction + 0 pts incorrect answer 1.3 1c 8 / 14 + 14 pts Correct, $$v_{3->1}=26.3*10^{15}Hz$$, $$v_{2->1}=22.2*10^{15}Hz$$, $$v_{3- >2}=4.1*10^{15}Hz$$ ✓ + 10 pts Two of the three frequencies correct + 6 pts One of the three frequencies correct + 2 pts $$E=hv$$ ✓ - 2 pts Math or unit error or incorrect answer QUESTION 2 2 25 pts 2.1 2a 10 / 10 ✓ + 10 pts Correct + 3 pts $$\psi(x)$$ vs x + 3 pts From $$-\frac {L}{2}$$ to $$\frac {L}{2}$$ + 4 pts Correct shape of curve + 0 pts No plot 2.2 2b 10 / 10 ✓ + 10 pts Correct + 3 pts $$\psi^2(x)$$ vs x + 3 pts From $$-\frac {L}{2}$$ to $$\frac {L}{2}$$ + 4 pts Correct shape of the curve + 0 pts No plot 2.3 2c 5 / 5 ✓ + 5 pts Correct, most probable x = $$-\frac {3L}{8}$$, $$-\frac {L}{8}$$, $$\frac {L}{8}$$, $$\frac {3L}{8}$$; least probable x = $$-\frac {L}{2}$$, $$- \frac {L}{4}$$,0, $$\frac {L}{4}$$, $$\frac {L}{2}$$ (can ignore the walls) + 3 pts Got one of the two sets (most probable or least probable) correct + 0 pts Click here to replace this description. + 0 pts Wrong bounds, 0 to L instead of -L/2 to L/2. QUESTION 3 3 3 13 / 15 ✓ + 15 pts Correct, $$\frac {P_V(a_0,\pi/2,\pi/2)}{P_V(a_0,\pi/4,\pi/4)}=14$$ or $$\frac {P_V(a_0,\pi/4,\pi/4)}{P_V(a_0,\pi/2,\pi/2)}=\frac {1}{14}=0.07$$ + 5 pts $$ P_{V,\, at \, r} = \int_{V,\, at \, r} (\psi_{2p_y}(r,\theta,\varphi))^2dV$$ + 5 pts $$ P_{V,\, at \, r} \approx (\psi_{2p_y}(r,\theta,\varphi))^2V$$ ✓ - 2 pts Math or unit error + 8 pts Only calculated one probability + 0 pts Click here to replace this description.

QUESTION 4 4 30 pts 4.1 4a 3 / 3 ✓ + 3 pts Correct, $$ \frac {kg}{s^2}$$, $$ \frac {N}{m}$$, $$ \frac {J}{m^2}$$ + 1 pts kgm/s^2, N, kg/s, J/m, kg/s^2*m + 0 pts wrong 4.2 4b 1 / 3 + 3 pts Correct, $$\frac {1}{m^2}$$, $$ \frac {kg}{J*s^2}$$, + 1 pts 1/m + 0 pts Blank/several errors in derivation + 1 pts kg*m/Js^2 / other close value/forgot square root ✓ + 1 pts confused m with meters, it is kg + 2 pts correct setup but not fully simplified/minor error + 1 pts h has units J*s 4.3 4c 2 / 6 + 6 pts Correct, $$ [\psi]=m^{-1/2} $$, $$ [\psi^2]=m^{-1} $$, $$ [\psi^2dx]=unitless\,\, probability $$ ✓ + 2 pts $$ [\psi]=m^{-1/2} $$ + 2 pts $$ [\psi^2]=m^{-1} $$ + 2 pts $$ [\psi^2dx]=unitless\,\, probability $$ + 0 pts wrong answer + 2 pts e has no units 4.4 4d 7 / 9 + 9 pts Correct, $$ P_{x>o}=\int_0^{\infty} P_o(x)dx=\frac {1}{2}$$ ✓ + 3 pts $$P= \int P_o(x)dx= \int \psi_o^2dx $$ ✓ + 4 pts $$ P_{x>o}=\int_0^{\infty} P_o(x)dx$$ + 2 pts $$P_{x>0}=\frac {1}{2}$$ + 5 pts Integrate from 0 to x but squared waveform + 2 pts Switched integration limits/did from -inf to inf + 0 pts Blank 4.5 4e 3 / 9 + 9 pts Correct, $$ PE = \frac {1}{4}h(\frac {1}{2\pi} \sqrt{\frac {k}{m}})=\frac {1}{4}hv=\frac {1}{2}E$$ ✓ + 3 pts $$PE=\int_{-\infty}^{\infty} (\frac {1}{2}kx^2)\psi_o^2dx$$ + 3 pts $$PE=\frac {1}{4}h(\frac {1}{2\pi} \sqrt{\frac {k}{m}})$$ + 3 pts $$PE=\frac {1}{2}E$$ + 0 pts Wrong answer/blank + 2 pts State PE is less than TE Page 2