Find the ratio of the binding energy per nucleon for helium (
) to uranium-238 (
) )
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 (

) to uranium-238 ( Find the ratio of the binding energy per nucleon for helium ( ) to uranium-238 ( ) ) Assume: M p = 1.007 825 u M n = 1.008 665 u MHe = 4.002 603 u MU = 238.050 786 u U = 1.66 × 10−27 kg A) 1.07 B) 0.934 C) 63.7 D) 1.6 × 10−2 E) 3.24

) )
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

Binding energy per nucleon is given by the formula: 
BE/A = [ZMp + (A-Z)Mn - M]/A 
where BE is the binding energy, A is the atomic mass number, Z is the atomic number, Mp is the mass of a proton, Mn is the mass of a neutron, and M is the mass of the nucleus.

For helium: 
BE/A = [(2)(1.007825 u) - 4.002603 u]/2 = 7.0739 MeV/nucleon

For uranium-238: 
BE/A = [(92)(1.007825 u) + (146)(1.008665 u) - 238.050786 u]/238 = 7.5928 MeV/nucleon

Therefore, the ratio of binding energy per nucleon for helium to uranium-238 is: 
7.0739/7.5928 ≈ 0.934

Hence, the best choice is B.

Find the Ratio of the Binding Energy Per Nucleon for Helium