JEE MainPhysicsNuclear Physics
Which of the following descriptions best represents the graph of nuclear mass density ( ) plotted against the mass number ( A ) of a nucleus?
Options
- AA horizontal straight line parallel to the A -axis
- BA straight line passing through the origin with a positive slope
- CA curve starting from the origin with a continuously decreasing positive slope
- DA curve with a negative slope that asymptotically approaches the A -axis
Correct answer
A. A horizontal straight line parallel to the A -axis
Step-by-step solution
The mass of a nucleus is directly proportional to its mass number A ( M A ). The volume of a nucleus is proportional to R^3 . Since the nuclear radius R A^ 1/3 , the volume is also proportional to A ( V A ). The nuclear mass density is the ratio of mass to volume: = M V Since both mass and volume are directly proportional to A , their ratio is a constant. Thus, the nuclear mass density is independent of the mass number A . Graphically, a quantity that remains constant with respect to an independent variable is repr