Prove analytically that the density of uranium nucleus is of the same order of magnitude as the density of hydrigen nucleus
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Atomic Nucleus
Problems from IIT JEE
Problem (IIT JEE 1999): Order of magnitude of density of uranium nucleus is, (Given R0≈1.1×10−15mR0≈1.1×10−15m and mp=1.67×10−27kgmp=1.67×10−27kg.)
1020kg/m31020kg/m31017kg/m31017kg/m31014kg/m31014kg/m31011kg/m31011kg/m3
Solution: Let AA be mass number of the uranium. The nuclear mass and the nuclear radius are given by,
m=Amp,R=R0A1/3≈1.1×10−15A1/3m.m=Amp,R=R0A1/3≈1.1×10−15A1/3m.
The nuclear density density is,
ρ=m43πR3=mp43πR30=1.67×10−2743×3.14×1.331×10−45≈3×1017kg/m3.ρ=m43πR3=mp43πR03=1.67×10−2743×3.14×1.331×10−45≈3×1017kg/m3.
Note that nuclear density is independent of A
Atomic Nucleus
Problems from IIT JEE
Problem (IIT JEE 1999): Order of magnitude of density of uranium nucleus is, (Given R0≈1.1×10−15mR0≈1.1×10−15m and mp=1.67×10−27kgmp=1.67×10−27kg.)
1020kg/m31020kg/m31017kg/m31017kg/m31014kg/m31014kg/m31011kg/m31011kg/m3
Solution: Let AA be mass number of the uranium. The nuclear mass and the nuclear radius are given by,
m=Amp,R=R0A1/3≈1.1×10−15A1/3m.m=Amp,R=R0A1/3≈1.1×10−15A1/3m.
The nuclear density density is,
ρ=m43πR3=mp43πR30=1.67×10−2743×3.14×1.331×10−45≈3×1017kg/m3.ρ=m43πR3=mp43πR03=1.67×10−2743×3.14×1.331×10−45≈3×1017kg/m3.
Note that nuclear density is independent of A
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