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Chapter 7: Problem 47

It takes \(7.21 \times 10^{-19} \mathrm{~J}\) of energy to remove an electron from an iron atom. What is the maximum wavelength of light that can do this?

Short Answer

Expert verified
The maximum wavelength of light capable of removing an electron from the iron atom is approximately \(275.6 \mathrm{~nm}\).

Step by step solution

01

Identify the relevant equations and constants

For this problem, we need the following equation: Planck's equation: \(E = h \times f\) where: - \(E\) is the energy of the light (in Joules), - \(h\) is the Planck's constant (\(6.626 \times 10^{-34} \mathrm{~J \cdot s}\)), - \(f\) is the frequency of the light (in Hertz). Also, we need the relation between frequency and wavelength of light: \(c = \lambda \times f\) where: - \(c\) is the speed of light (\(3.0 \times 10^8 \mathrm{~m/s}\)), - \(\lambda\) is the wavelength of the light (in meters).
02

Express the frequency in terms of energy

Now we will solve the Planck's equation for the frequency: \(\Rightarrow f = \frac{E}{h}\)
03

Replace the energy value in the equation

Now replace the given energy value in the equation: \(f = \frac{7.21 \times 10^{-19} \mathrm{~J}}{6.626 \times 10^{-34} \mathrm{~J \cdot s}}\)
04

Calculate the frequency

Now calculate the frequency, giving: \(f \approx 1.088 \times 10^{15} \mathrm{~Hz}\)
05

Relate frequency and wavelength

Now we will use the relation between frequency and wavelength: \(\lambda = \frac{c}{f}\)
06

Compute the maximum wavelength

Now substitute the frequency value and speed of light into the equation to find the maximum wavelength: \(\lambda = \frac{3.0 \times 10^8 \mathrm{~m/s}}{1.088 \times 10^{15} \mathrm{~Hz}}\) \(\lambda \approx 2.756 \times 10^{-7} \mathrm{~m}\) Since the wavelength is often expressed in nanometers, we can convert the result: \(\lambda = 2.756 \times 10^{-7} \mathrm{~m} \times \frac{10^9 \mathrm{~nm}}{1\mathrm{~m}} \approx 275.6 \mathrm{~nm}\) Therefore, the maximum wavelength of light capable of removing an electron from the iron atom is approximately \(275.6 \mathrm{~nm}\).

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Most popular questions from this chapter

Francium, Fr, is a radioactive element found in some uranium minerals and is formed as a result of the decay of actinium. a. What are the electron configurations of francium and its predicted most common ion? b. It has been estimated that at any one time, there is only one (1.0) ounce of francium on earth. Assuming this is true, what number of francium atoms exist on earth? c. The longest-lived isotope of francium is \({ }^{223} \mathrm{Fr}\). What is the total mass in grams of the neutrons in one atom of this isotope?

The elements \(\mathrm{Cu}, \mathrm{O}, \mathrm{La}, \mathrm{Y}, \mathrm{Ba}, \mathrm{Tl}\), and \(\mathrm{Bi}\) are all found in high- temperature ceramic superconductors. Write the expected electron configuration for these atoms.

Give a possible set of values of the four quantum numbers for all the electrons in a boron atom and a nitrogen atom if each is in the ground state.

Arrange the following groups of atoms in order of increasing size. a. \(\mathrm{Rb}, \mathrm{Na}, \mathrm{Be}\) b. \(\mathrm{Sr}, \mathrm{Se}, \mathrm{Ne}\) c. \(\mathrm{Fe}, \mathrm{P}, \mathrm{O}\)

Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at \(1.00 \%\) of the speed of light. b. Calculate the velocity of a neutron with a wavelength of \(75 \mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{~m}\right)\)
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