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Wave Optics

Question
CBSEENPH12039144

a) In a typical nuclear reaction, e.g. , Error converting from MathML to accessible text.

Although number of nucleons is conserved, yet energy is released. How? Explain.

b) Show that nuclear density in a given nucleus is independent of mass number A.

Solution

a) 
In a nuclear reaction, 

                           Error converting from MathML to accessible text.

In a nuclear reaction, the sum of the masses of the of the target nucleus and the bombarding particle may be greater or less than the sum of masses of the product nucleus and the outgoing particle. Therefore, from the law of conservation of mass-energy around 3.27 MeV is evolved or involved in a nuclear reaction. This energy is called the Q-value of the nuclear reaction.

Cause of the energy released:

i) Binding energy per nucleon of  becomes more than the BE/A of H presubscript 1 presuperscript 2 
ii) Mass defect between the reactant and the product nuclei.

b) The radius of nucleus of mass number A is given by R = R subscript o A to the power of bevelled 1 third end exponent
Volume of the nucleus, V space equals space 4 over 3 pi R cubed space equals 4 over 3 pi R subscript o cubed space A 
Density of the matter in the nucleus is given by, 
                              straight rho space equals space space Mass divided by Volume

space space space equals fraction numerator A left parenthesis u right parenthesis over denominator 4 over 3 pi R subscript o cubed A end fraction
space space space equals fraction numerator 1 over denominator 4 over 3 pi R subscript o cubed end fraction

space space space space equals fraction numerator 3 over denominator 4 πR subscript straight o cubed end fraction 
Hence, density is independent of mass number A.

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