/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 The binding energies of the atom... [FREE SOLUTION] | 91影视

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Chapter 19: Problem 8

The binding energies of the atoms of elements \(A\) and \(B\) are \(E_{a}\) and \(E_{b}\) respectively. Three atoms of the element \(B\) fuse to give one atom of element \(A\). This fusion process is accompanied by release of energy \(e\). Then \(E_{a}\), \(E_{b}\) and \(e\) are related to each other as (A) \(E_{a}+e=3 E_{b}\) (B) \(E_{a}=3 E_{b}\) (C) \(E_{a}-e=3 E_{b}\) (D) \(E_{a}+3 E_{b}+e=0\)

Short Answer

Expert verified
The correct answer is (A) \(E_{a}+e=3 E_{b}\), as it matches the energy equation obtained by applying the conservation of energy principle.

Step by step solution

01

Analyze the information given in the problem.

We are given the following information: - Binding energy of the atoms of elements A and B are \(E_a\) and \(E_b\) respectively. - 3 atoms of element B fuse together to form 1 atom of element A. - The energy released during this fusion process is "e".
02

Apply the conservation of energy principle of and write down the energy equation.

According to the conservation of energy principle, the sum of the initial energies should be equal to the sum of the final energies. Initial energies: - 3 atoms of element B each with binding energy \(E_b\), so the total initial energy is \(3E_b\). Final energies: - 1 atom of element A with binding energy \(E_a\). - Released energy "e" during the fusion process. Writing the energy equation, we have: Initial Energy = Final Energy \(3E_b = E_a + e\)
03

Select the correct option matching the above energy equation.

Comparing our equation \(3E_b = E_a + e\) to the given options, we see that it matches with option (A): \(E_{a}+e=3 E_{b}\) Thus, the correct answer is (A).

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Most popular questions from this chapter

The electron in a hydrogen atom makes a transition \(n_{1} \rightarrow n_{2}\), where \(n_{1}\) and \(n_{2}\) are the principal quantum numbers of two states. Assume the Bohr model to be valid. If the time period of the electron in the initial state is eight times that in the final state then the possible values of \(n_{1}\) and \(n_{2}\) are (A) \(n_{1}=4, n_{2}=2\) (B) \(n_{1}=8, n_{2}=2\) (C) \(n_{1}=8, n_{2}=1\) (D) \(n_{1}=6, n_{2}=3\)

The binding energy per nucleon for the parent nucleus is \(E_{1}\) and that for the daughter nuclei is \(E_{2}\). Then (A) \(E_{1}=2 E_{2}\) (B) \(E_{2}=2 E_{1}\) (C) \(E_{1}>E_{2}\) (D) \(E_{2}>E_{1}\)

Which of the following statement about \(x\)-rays is/are true? (A) \(E\left(K_{\alpha}\right)+E\left(L_{\beta}\right)=E\left(K_{\beta}\right)+E\left(M_{\alpha}\right)=E\left(K_{\gamma}\right)\), where \(E\) is the energy of respective \(x\)-rays. (B) For the harder \(x\)-rays, the intensity is higher than soft \(x\)-rays. (C) The continuous and the characteristic \(x\)-rays differ only in the method of creation. (D) The cut-off wavelength \(\lambda_{\min }\) depends only on the accelerating voltage applied between the target and the filament.

Energy required for the electron excitation in \(\mathrm{Li}^{++}\) from the first to the third Bohr orbit is (A) \(12.1 \mathrm{eV}\) (B) \(36.3 \mathrm{eV}\) (C) \(108.8 \mathrm{eV}\) (D) \(122.4 \mathrm{eV}\)

An electron in hypothetical hydrogen atom is in its \(3^{\text {rd }}\) excited state and makes transition from \(3^{\text {rd }}\) to \(2^{\text {nd }}\) excited, then to \(1^{\text {st }}\) excited state and then to ground state. If the amount of time spent by the electron in any state of quantum number \(n\), is proportional to \(\left(\frac{1}{n-1}\right)\), then the ratio of number of revolutions completed by the electron in \(1^{\text {st }}\) excited state to that in the \(2^{\text {nd }}\) excited state will be (A) 2 (B) \(\frac{27}{8}\) (C) \(\frac{27}{4}\) (D) \(\frac{27}{6}\)
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