Find the ratio of the binding energy per nucleon for helium ( ${ } _ { 2 } ^ { 4 } \mathrm { He }$ ) to uranium-238 ( ${ } _ { 92 } ^ { 238 } \mathrm { U }$ ) . Assume:
M_p = 1.007 825 u
M_n = 1.008 665 u
M_He = 4.002 603 u
M_U = 238.050 786 u
U = 1.66 *10 ^- ²⁷ kg

Question

Find the ratio of the binding energy per nucleon for helium (

{ } _ { 2 } ^ { 4 } \mathrm { He }

) to uranium-238 (

{ } _ { 92 } ^ { 238 } \mathrm { U }

) . Assume:
M_p = 1.007 825 u
M_n = 1.008 665 u
M_He = 4.002 603 u
M_U = 238.050 786 u
U = 1.66 *10 ^- ²⁷ kg

Quizplus · Accepted Answer

The binding energy per nucleon can be calculated using the formula E/A, where E is the binding energy and A is the number of nucleons. Using the given data, the binding energy per nucleon for helium is:

E He = 2 × 4.002603 u - 4.030387 u = 28.30 MeV
E/A He = 28.30 MeV / 2 = 14.15 MeV/nucleon

Similarly, the binding energy per nucleon for uranium-238 is:

E U = 238 × 238.050786 u - 238.908931 u = 1785.93 MeV
E/A U = 1785.93 MeV / 238 = 7.49 MeV/nucleon

The ratio of E/A for helium to uranium-238 is:

(E/A He) / (E/A U) = (14.15 MeV/nucleon) / (7.49 MeV/nucleon) = 1.888

Therefore, the closest answer choice is B) 0.934, which is the inverse of the calculated ratio.

Find the Ratio of the Binding Energy Per Nucleon for Helium