Question

If mass of 5 neutrons is x, mass of 2 protons is y and the mass of the nucleus $_{10}X^{20}$ is z, then the binding energy of the nucleus X is (Speed of light in vacuum is c)

• A. $[10y+10x-z]c^2$
• B. $[z-5y-2x]c^2$
• C. $[5y+2x-z]c^2$
• D. $[z-10y-10x]c^2$

Hint:

Binding Energy is the energy released when nucleons come together to form a nucleus, accounting for the "missing mass" (mass defect).

Answer 1

The Correct Option is C

Step 1: Nuclear Composition:
Nucleus $_{10}X^{20}$ has: Atomic Number $Z = 10$ (Protons). Mass Number $A = 20$. Neutron Number $N = A - Z = 20 - 10 = 10$ (Neutrons).
Step 2: Total Mass of Constituents:
Given: Mass of 5 neutrons = $x \Rightarrow$ Mass of 1 neutron $m_n = x/5$. Mass of 2 protons = $y \Rightarrow$ Mass of 1 proton $m_p = y/2$. Total mass of 10 neutrons $= 10 \times (x/5) = 2x$. Total mass of 10 protons $= 10 \times (y/2) = 5y$. Total constituent mass $= 5y + 2x$.
Step 3: Mass Defect ($\Delta m$):
Mass defect = (Mass of constituents) - (Mass of nucleus). Given mass of nucleus = $z$. \[ \Delta m = (5y + 2x) - z \]
Step 4: Binding Energy:
\[ BE = \Delta m c^2 = [5y + 2x - z]c^2 \]
Step 5: Final Answer:
The binding energy is $[5y+2x-z]c^2$.