### Part A Using the equation: \[ E = (hcR_H) \left(\frac{1}{n^2}\right) = \left(-2.18 \times 10^{-18} \, \text{J}\right) \left(\frac{1}{n^2}\right) \] calculate the energy of an electron in the hydrogen atom when \( n = 2 \). **Express your answer in joules to three significant figures.** **Input Box:** \( E_2 = \) ______ J **[Submit] [Request Answer]** --- This task involves using the formula for the energy levels of electrons in a hydrogen atom. The equation calculates the energy in joules, where: - \( h \) is Planck's constant, - \( c \) is the speed of light, - \( R_H \) is Rydberg's constant, - \( n \) is the principal quantum number. You need to substitute \( n = 2 \) into the formula to find the energy level of the electron. **Part B** Using the equation \[ E = (hcR_H) \left(\frac{1}{n^2}\right) = (-2.18 \times 10^{-18} \, \text{J}) \left(\frac{1}{n^2}\right) \] calculate the energy of an electron in the hydrogen atom when \( n = 4 \). **Express your answer in joules to three significant figures.** \[ E_4 = \boxed{\phantom{0}} \, \text{J} \]

### Part A Using the equation: \[ E = (hcR_H) \left(\frac{1}{n^2}\right) = \left(-2.18 \times 10^{-18} \, \text{J}\right) \left(\frac{1}{n^2}\right) \] calculate the energy of an electron in the hydrogen atom when \( n = 2 \). Express your answer in joules to three significant figures. Input Box: \( E_2 = \) ______ J [Submit] [Request Answer] --- This task involves using the formula for the energy levels of electrons in a hydrogen atom. The equation calculates the energy in joules, where: - \( h \) is Planck's constant, - \( c \) is the speed of light, - \( R_H \) is Rydberg's constant, - \( n \) is the principal quantum number. You need to substitute \( n = 2 \) into the formula to find the energy level of the electron. Part B Using the equation \[ E = (hcR_H) \left(\frac{1}{n^2}\right) = (-2.18 \times 10^{-18} \, \text{J}) \left(\frac{1}{n^2}\right) \] calculate the energy of an electron in the hydrogen atom when \( n = 4 \). Express your answer in joules to three significant figures. \[ E_4 = \boxed{\phantom{0}} \, \text{J} \]

Chemistry: Principles and Practice

3rd Edition

ISBN:9780534420123

Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Chapter7: Electronic Structure

Section: Chapter Questions

Problem 7.65QE

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Similar questions

Which of the following is a valid set of quantum numbers for an electron in a hydrogen atom? (a) n = 1, = 0, m = 0, ms = 1 (b) n = 1, = 1, m = 0, ms = 1/2 (c) n = 1, = 0, m = 1, ms = + 1/2 (d) n = 1, = 0, m = 0, ms = 1/2
Which of the following sets of quantum numbers correctly represents a 4p orbital? (a) n = 4, = 0, m = 1 (b) n = 4, = 1, m = 0 (c) n = 4, = 2, m = 1 (d) n = 4, = 1, m =2
(a) Use the radial wave function for the 3p orbital of a hydrogen atom (see Table 5.2) to calculate the value of r for which a node exists. (b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom.
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
What is the maximum number of electrons that can occupy a f subshell (l = 3)?
According to a relationship developed by Niels Bohr, for an atom or ion that has a single electron, the total energy, En, of an electron in a stable orbit of quantum number n is En = [Z2/n2] (2.179 1018 J) where Z is the atomic number. Calculate the ionization energy for the electron in a ground-state He+ ion.
Investigating Energy Levels Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation E=RHn3 where RH is the same as for hydrogen (2.179 1018 J). Answer the following questions, without calculating energy values. a How would the ground-state energy levels of X and H compare? b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer. c How do the spacings of the energy levels of X and H compare? d Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? e Which atom, X or H, would require more energy to completely remove its electron? f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.
Order the atoms in each of the following sets from the least negative electron affinity to the most. a. N, O, F b. Al, Si, P
6.96 When a helium atom absorbs light at 58.44 nm, an electron is promoted from the 1s orbital to a 2p orbital. Given that the ionization energy of (ground state) helium is 2372 kJ/ mol, find the longest wavelength of light that could eject an electron from the excited state helium atom.
Spectroscopists have observed He+ in outer space. This ion is a one-electron species like a neutral hydrogen atom. Calculate the energy of the photon emitted for the transition from the n = 5 to the n = 3 state in this ion using the equation: En = − Z2/n2 (2.179 × 10−18 J). Z is the positive charge of the nucleus and n is the principal quantum number. In what part of the electromagnetic spectrum does this radiation lie?