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Chapter 3: Problem 99

Energy of H-atom in the ground state is \(-13.6 \mathrm{eV}\), hence energy in the second excited state is a. \(-6.8 \mathrm{eV}\) b. \(-3.4 \mathrm{eV}\) c. \(-1.51 \mathrm{eV}\) d. \(-4.53 \mathrm{eV}\)

Short Answer

Expert verified
The energy in the second excited state is -1.51 eV.

Step by step solution

01

Understanding Energy Levels

The energy levels of the hydrogen atom are given by the formula \[ E_n = - rac{13.6 ext{ eV}}{n^2} \] where \( n \) is the principal quantum number. The ground state corresponds to \( n = 1 \), which is given as -13.6 eV. Our goal is to find the energy of the second excited state.
02

Identifying Second Excited State

The first excited state corresponds to \( n = 2 \), and the second excited state corresponds to \( n = 3 \). We are tasked to find the energy when \( n = 3 \).
03

Calculating Energy for n=3

Substitute \( n = 3 \) into the equation:\[ E_3 = -\frac{13.6 ext{ eV}}{3^2} = -\frac{13.6 ext{ eV}}{9} \]Calculate this value to find the energy in the second excited state.
04

Simplifying and Result

Evaluating the expression:\[ E_3 = -\frac{13.6 ext{ eV}}{9} = -1.51 ext{ eV} \]Thus, the energy of the hydrogen atom in the second excited state is -1.51 eV.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ground State Energy
The concept of ground state energy is fundamental when discussing atomic structures, particularly with the hydrogen atom. In chemistry and physics, the ground state refers to the lowest possible energy level of an electron within an atom.

For a hydrogen atom, this lowest energy level is when the electron is closest to the nucleus. This state is denoted by the principal quantum number, \( n = 1 \).

The energy associated with this state, known as the ground state energy, is a specific value for hydrogen: \(-13.6\ \mathrm{eV}\). This value indicates that it requires 13.6 electron volts (\

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Most popular questions from this chapter

Which of the following statement(s) are correct? 1\. the electronic configuration of \(\mathrm{Cr}\) is \([\mathrm{Ar}] 3 \mathrm{~d}^{5}\) \(4 \mathrm{~s}^{1}\) (atomic number of \(\mathrm{Cr}=24\) ) 2\. the magnetic quantum number may have a negative value 3\. in silver atom, 23 electrons have a spin of one type and 24 of the opposite type (atomic number of \(\mathrm{Ag}=47\) ) 4\. the oxiation state of nitrogen in \(\mathrm{HN}_{3}\) is \(-3\). a. \(1,2,3\) b. \(2,3,4\) c. 3,4 d. \(1,2,4\)

The correct matching is shown by a. Wave mechanical model: The electron finding probability for 2 s orbital in H-atom is zero at \(\mathrm{r}=\mathrm{a}_{0}\) where \(\mathrm{a}_{0}=0.53 \mathrm{~A}\). b. Bohr's model: The angular momentum of electron in first excited state of \(\mathrm{H}\)-atom is \(5 \mathrm{~h} / 11\) c. Rutherford's model : Very few \(\alpha\)-particles get deflected by large angles because nucleus has much smaller volume than that of atom d. Thomson's model: The electrons on disturbing by collision vibrate around their mean position and emit electromagnetic radiation.

(A): On heating a solid for a longer time, radiations become white and then blue as the temperature becomes very high. (R): Radiations emitted go from a lower frequency to higher frequency as the temperature increases.

Which of the following statement(s) about spectral series is/are correct? a. Paschen series appears in the infrared region b. The lines in the Balmer series corresponds to electron transitions from energy levels higher than \(\mathrm{n}=2\) energy level. c. Transitions from higher energy levels to \(5^{\text {th }}\) energy level produce Pfund series which falls in the infrared region d. The lines of Lyman series appear in the visible region

Which statement is/are true for many electron atoms? a. The \(2 \mathrm{Px}\) and \(2 \mathrm{Py}\) orbitals have the same energy in the absence of an applied magnetic field b. The 2 s and \(2 p\) orbitals are of differing energies, whereas in a hydrogen atom they are same. c. Outer electrons penetrate the electron clouds of inner electrons d. Outer electrons experience the full nuclear charge
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