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Chapter 38: Q. 54 (page 1116)

Consider a small virus having a diameter of 10 nm. The atoms of the intracellular fluid are confined within the virus. Suppose we model the virus as a 10-nm-long “box.” What is the ground state energy (in eV) of a sodium ion confined in this box?

Short Answer

Expert verified

The ground state energy (in eV) of a sodium ion isE1=9×10−8eV

Step by step solution

01

Given information

Consider a tiny virus with a 10 nm diameter. Within the virus, the atoms of the internal fluid are contained.

02

Determine ground state energy  of a sodium ion 

We can begin by expressing the energy of a particle in a box as follows:

En=n2h28mL2n=1(ground state energy)E1=12×6.63×10−3428×3×82×10−26×10×10−92(substitute)E1=1.44×10−26J=9×10−8eV

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Most popular questions from this chapter

FIGURE Q38.5 is the current-versus-potential-difference graph for a photoelectric-effect experiment with an unknown metal. If classical physics provided the correct description of the photoelectric effect, how would the graph look if:

a. The light was replaced by an equally intense light with a shorter wavelength? Draw it.

b. The metal was replaced by a different metal with a smaller work function? Draw it.

Which metals in Table 38.1 exhibit the photoelectric effect for (a) light withλ=400nm and (b) light with λ=250nm?

(a). What is the de Broglie wavelength of a 200gbaseball with a speed of 30m/s?

(b). What is the speed of a 200gbaseball with a de Broglie wavelength of 0.20nm?

I FIGURE EX38.24 is an energy-level diagram for a simple atom. What wavelengths, in \mathrm{nm}, appear in the atom's (a) emission spectrum and (b) absorption spectrum?

n=3⟶E3=4.00eV

n=2-E2=1.50eV

FIGURE EX38.24 n=1-E_{1}=0.00 \mathrm{eV}

The graph in FIGURE P 38.42was measured in a photoelectric effect experiment.

a. What is the work function (in eV) of the cathode?

b. What experimental value of Planck’s constant is obtained from these data?
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