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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

A hot bar of iron glows a dull red. Using our simple ball-spring model of a solid (Figure 8.23), answer the following questions,explaining in detail the processes involved. You will need to make some rough estimates of atomic properties based on prior work. (a) What is the approximate energy of the lowest-energy spectral emission line? Give a numerical value. (b) What is the approximate energy of the highest-energy spectral emission line? Give a numerical value. (c) What is the quantum number of the highest-energy occupied state? (d) Predict the energies of two other lines in the emission spectrum of the glowing iron bar. (Note: Our simple model is too simple-the actual spectrum is more complicated. However, this simple analysis gets at some important aspects of the phenomenon.)

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?

The photon energy for green light lies between the values for red and violet light. What is the approximate energy of the photons in green light? The intensity of sunlight above the Earth鈥檚 atmosphere is about 1400 W (J/s) per square meter. That is, when sunlight hits perpendicular to a square meter of area, about 1400 W of energy can be absorbed. Using the photon energy of green light, about how many photons per second strike an area of one square meter? (This is why the lumpiness of light was not noticed for so long.)

Match the description of a process with the corresponding arrow in figure 8.38: (a) Absorption of a photon whose energy is E1-E0. (b) Absorption from an excited state (a rare event at ordinary temperatures). (c) Emission of a photon whose energy isE3-E1 . (d) Emission of a photon whose energy isE2-E0 . (e) In drawing arrows to represent energy transitions, which of the following statement are correct. (1) it doesn鈥檛 matter in which direction you draw the arrow as long as it connects the initial and final states. (2) For emission, the arrow points down. (3) For absorption, the arrow points up. (4) The tail of the arrow is drawn on the initial state. (5) The head of the arrow is drawn on the final state. (6) It is not necessary to draw and arrowhead.

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.)
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