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Chapter 8: Q12P (page 344)

N=1 is the lowest electronic energy state for a hydrogen atom. (a) If a hydrogen atom is in a state N=4, what is K+U for this atom (in eV)? (b) The hydrogen atom makes a transition to state N=2, Now what is K+U in electron volts for this atom? (c) What is energy (in eV) of the photon emitted in the transition from level N=4 to N=2? (d) Which of the arrows in figure 8.40 represents this transition?

Short Answer

Expert verified

The total energy level in the fourth level is -0.85eV.

Step by step solution

01

Identification of given data

The state of hydrogen atom is N=4

02

Conceptual Explanation

The energy of an atom at a particular level varies with the level of the atom. The energy in the lowest level of hydrogen atom is 13.6 eV.

03

Determination of total energy of hydrogen atom

The total energy of hydrogen atom is given as:

K+UN=-13.6eVN2

Substitute all the values in the above equation.

K+U4=-13.6eV42K+U4=-0.85eV

Therefore, the total energy of hydrogen is -0.85eV

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Most popular questions from this chapter

For a certain diatomic molecule, the lowest-energy photon observed in the vibrational spectrum is 0.17eV. What is the energy of a photon emitted in a transition from the 5th excited vibrational energy level to the 2nd excited vibrational energy level, assuming no change in the rotational energy?

The mean lifetime of a certain excited atomic state is 5 ns. What is the probability of the atom staying in this excited state for t=10 ns or more?

Make a rough estimate of this uniform energy spacing in electron volts (where 1鈥�eV=1.6脳10鈭�19鈥塉). You will need to make some rough estimates of atomic properties based on prior work. For comparison with the spacing of these vibrational energy states, note that the spacing between quantized energy levels for "electronic" states such as in atomic hydrogen is of the order of several electron volts.

(b) List several photon energies that would be emitted if a number of these vibrational energy levels were occupied due to collisional excitation. To what region of the spectrum (x-ray, visible, microwave, etc.) do these photons belong? (See Figure 8.1 at the beginning of the chapter.)

Energy graphs: (a) Figure 8.41 shows a graph of potential energy vs. interatomic distance for a particular molecule. What is the direction of the associated force at location A? At location B? At location C? Rank the magnitude of the force at locations A,B and C. (That is, which is greatest , which is smallest, and are any of these equal to each other?) For the energy level shown on the graph, draw a line whose height is the kinetic energy when the system is at location D.

(b) Figure 8.42 shows all of the quantized energies (bound states) for one of these molecules. The energy for each state is given on the graph, in electron volts ( 1鈥�eV=1.6脳10鈭�19鈥�J). How much energy is required to break a molecule apart, if it is initially in the ground state? (Note that the final state must be an unbound state; the unbound states are not quantized.)

(c) At high enough temperatures, in a collection of these molecules there will be at all times some molecules in each of these states, and light will be emitted. What are the energies in electron volts of the emitted light?

(d) The "inertial" mass of the molecule is the mass that appears in Newton's second law, and it determines how much acceleration will result from applying a given force. Compare the inertial mass of a molecule in the ground state and the inertial mass of a molecule in an excited state10鈥�eV above the ground state. If there is a difference, briefly explain why and calculate the difference. If there isn't a difference, briefly explain why not.)

What is the energy of the photon emitted by the harmonic oscillator with stiffness ks and mass m when it drops from energy level 5 to energy level 2?
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