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Chapter 39: Q38P (page 1216)

6.2×1014HzAn atom (not a hydrogen atom) absorbs a photon whose associated frequency is . By what amount does the energy of the atom increase?

Short Answer

Expert verified

The energy of the atom is increased by 4.12×10-19J.

Step by step solution

01

The energy of the photon:

The expression of the energy of the photon is given by,

∆E=hf ….. (1)

Here, h is plank constant, and f is frequency of the photon.

02

Define the amount of increase in the energy of the atom:

Substitute 6.626×10-34J.sfor h, and 6.2×1014Hzfor f in equation (1).

∆E=6.626×10-34J.s6.2×1014Hz=4.12×10-19J

Hence, the energy of the atom is increased by 4.12×10-19J.

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Most popular questions from this chapter

An atom (not a hydrogen atom) absorbs a photon whose associated wavelength is 375 nm and then immediately emits a photon whose associated wavelength is 580 nm . How much net energy is absorbed by the atom in this process?

Calculate the radial probability density P(r) for the hydrogen atom in its ground state at (a) r = 0 , (b) r = a , and (c) r = 2a, where a is the Bohr radius.

A diatomic gas molecule consists of two atoms of massseparated by a fixed distance drotating about an axis as indicated in given figure. Assuming that its angular momentum is quantized as in the Bohr model for the hydrogen atom, find

  1. The possible angular velocities.
  2. The possible quantized rotational energies.

Figure 39-30 shows a two-dimensional, infinite-potential well lying in an xy plane that contains an electron. We probe for the electron along a line that bisects Lxand find three points at which the detection probability is maximum. Those points are separated by 2.00 nm . Then we probe along a line that bisects Lyand find five points at which the detection probability is maximum. Those points are separated by 3.00 nm . What is the energy of the electron?

The wave function for the hydrogen-atom quantum state represented by the dot plot shown in Fig. 39-21, which has n = 2 and l=ml=0, is

Ψ200(r)=142πa-3/2(2-ra)e-r/2a

in which a is the Bohr radius and the subscript onΨ(r)gives the values of the quantum numbers n,l,ml. (a) PlotΨ(2002r)and show that your plot is consistent with the dot plot of Fig. 39-21. (b) Show analytically thatΨ(2002r)has a maximum at r=4a. (c) Find the radial probability densityP200(r)for this state. (d) Show that

∫0∞P200(r)dr=1

and thus that the expression above for the wave function Ψ200(r)has been properly normalized.
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