Question

The binding energy per nucleon of uranium in Mev is
(Atomic mass of uranium mass = 238.0508 amu; mass of hydrogen atom is MH = 1.0078 amu Mass of neutron mn = 1.0087 amu; atomic number of Uranium z = 92; Mass number of uranium A = 238)
 A.7.580
 B.6.216
 C.5.162
 D.3.146

Answer 1

Hint In order to solve this problem we need to find the binding energy per nucleon for Uranium.to calculate the binding energy per nucleon at first calculate the change in mass that is$\Delta m$, and then calculate the binding energy.
To find BE/nucleon, we need to divide BE by the mass of uranium to get the final result.

Complete step-by-step solution
No. of proton of uranium = 92.(protons are equal to the atomic number of elements)
No. of neutrons = (mass number − Atomic number)
          = 238 − 92
          = 146.
Now, we need to find the (change in mass) for which we have to use
     $\Delta m$= no. of protons × mass of hydrogen atom + no of neutrons mass of neutron − atomic mass of uranium.
       = [92 × 1.0078 + 146 × 1.0087 −238.0508]
$\Delta m$ = 1937 amu
Now that we have calculated $\Delta m$we need to find the Binding energy (B.E)
B.E = 1.937 × 931.478 Mev
      = 1804.27 Mev
 the BE of uranium = 1804.27 Mev
To find BE/nucleon, we need to divide BE by the mass of uranium
BE/nucleon $\begin{align}
  & =\dfrac{1804.27}{238}\text{Mev} \\
 & =7.58\ \text{Mev} \\
\end{align}$
 BE/nucleon of uranium $=7.58\text{Mev}$

Hence option 'a' is the correct answer for this question

Note The BE per nucleon is always a positive number. The formula is simple but we need to remember the atomic number, mass number very correctly for its calculation.