   Chapter 25, Problem 62GQ

Chapter
Section
Textbook Problem

When a neutron is captured by an atomic nucleus, energy is released as γ radiation. This energy can be calculated based on the change in mass in converting reactants to products.For the nuclear reaction L 3 6 i +  n 0 1 → L 3 7 i +  γ :(a) Calculate the energy evolved in this reaction (per atom). Masses needed (in g/mol) are L 3 6 i = 6.01512, n 0 1 = 1.00867, and L 3 7 i = 7.01600.n(b) Use the answer in part (a) to calculate the wave-length of the γ rays emitted in the reaction.

(a)

Interpretation Introduction

Interpretation:

The energy involved in the given nuclear reaction has to be calculated.

Concept introduction: In the radioactive decay process the unstable isotopes loses their energy by emitting radiation in order to attain stable species. It is converted in to stable isotopes by emitting positron +10β , gamma 00γ , Beta β10, alpha 24He and or by electron capture 10e .

Isotopes: The two elements with same atomic number but with different mass number are considered as isotopes of each other.

Binding energy: It is defined as the energy needed by an atom or molecule to completely loss one electron from it. The binding energy of an atom is calculated as,

Eb= (Δm)c2,whereEb= BindingenergyΔm = massdefect = mass of products - mass of reactantsc = velocityoflight

Explanation

Given,

The masses needed are

L36i=6.01512n01=1.00867L37i=7.01600

By using Binding energy formula

Eb=(Δm)c2

Here Δm=mass of products-mass of reactants

Δm =  7.01600 - (6.01512+1

(b)

Interpretation Introduction

Interpretation:

The wave length for Gamma rays emitted in the given reaction has to be calculated.

Concept introduction:

In the radioactive decay process the unstable isotopes loses their energy by emitting radiation in order to attain stable species. It is converted in to stable isotopes by emitting positron +10β , gamma 00γ , Beta β10, alpha 24He and or by electron capture 10e .

Isotopes: The two elements with same atomic number but with different mass number are considered as isotopes of each other.

Binding energy: It is defined as the energy needed by an atom or molecule to completely loss one electron from it. The binding energy of an atom is calculated as,

Eb= (Δm)c2,whereEb= BindingenergyΔm = massdefect = mass of products - mass of reactantsc = velocityoflight

The equation for energy of photon is given by

E = hυ= hcλλ = hcE

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