Example 13.1intermediate🔧 Apply2 marksNumerical

Given the mass of iron nucleus as 55.85u and A=56, find the nuclear density?

Example 13.2beginner🔧 Apply2 marksNumerical

Calculate the energy equivalent of 1 g of substance.

Example 13.3intermediate🔧 Apply3 marksNumerical

Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV. Using this, express the mass defect of $^{16}_{8}\text{O}$ in MeV/ $c^2$ .

Example 13.4intermediate🔍 Analyze3 marksLong Answer

Answer the following questions:

13.1intermediate🔧 Apply2 marksNumerical

Obtain the binding energy (in MeV) of a nitrogen nucleus $^{14}_{7}\text{N}$ , given $m(^{14}_{7}\text{N}) = 14.00307 \text{u}$

13.2intermediate🔧 Apply3 marksNumerical

Obtain the binding energy of the nuclei $^{56}_{26}\text{Fe}$ and $^{209}_{83}\text{Bi}$ in units of MeV from the following data:

m(^{56}_{26}\text{Fe}) = 55.934939 \text{u}

m(^{209}_{83}\text{Bi}) = 208.980388 \text{u}

13.3intermediate🔧 Apply3 marksNumerical

A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of $^{63}_{29}\text{Cu}$ atoms (of mass 62.92960 u).

13.4beginner🔧 Apply2 marksNumerical

Obtain approximately the ratio of the nuclear radii of the gold isotope $^{197}_{79}\text{Au}$ and the silver isotope $^{107}_{47}\text{Ag}$ .

13.6intermediate🔍 Analyze3 marksNumerical

Suppose, we think of fission of a $^{56}_{26}\text{Fe}$ nucleus into two equal fragments, $^{28}_{13}\text{Al}$ . Is the fission energetically possible? Argue by working out $Q$ of the process. Given $m(^{56}_{26}\text{Fe}) = 55.93494 \text{u}$ and $m(^{28}_{13}\text{Al}) = 27.98191 \text{u}$ .

13.7intermediate🔧 Apply3 marksNumerical

The fission properties of $^{239}_{94}\text{Pu}$ are very similar to those of $^{235}_{92}\text{U}$ . The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure $^{239}_{94}\text{Pu}$ undergo fission?

13.8intermediate🔧 Apply3 marksNumerical

How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as

^{2}_{1}\text{H} + ^{2}_{1}\text{H} \rightarrow ^{3}_{2}\text{He} + n + 3.27\text{MeV}

13.9advanced🔧 Apply3 marksNumerical

Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.)

13.10beginner💡 Understand2 marksShort Answer

From the relation $R = R_0 A^{1/3}$ , where $R_0$ is a constant and $A$ is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of $A$ ).

Nuclei

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