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Chapter 7: Problem 55

The work function of an element is the energy required to remove an electron from the surface of the solid element. The work function for lithium is 279.7 kJ/mol (that is, it takes 279.7 kJ of energy to remove one mole of electrons from one mole of Li atoms on the surface of Li metal). What is the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal?

Short Answer

Expert verified
The maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal is about 428.2 nm. This is calculated by first converting the work function of lithium to energy per electron in joules, and then using Planck's equation to find the corresponding wavelength of light.

Step by step solution

01

Convert the work function to energy per electron in joules

Given that the work function for lithium is 279.7 kJ/mol, we first need to convert it into energy per electron in joules. We can do this by dividing the given value by Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms/mol) and then converting it from kJ to J by multiplying with 1000. Energy per electron (J) = \(\frac{279.7 \: \text{kJ/mol}}{6.022 \times 10^{23} \: \text{atoms/mol}}\times 1000 \: \text{J/ kJ}\)
02

Calculate the energy per electron in joules

Now, let's calculate the energy per electron using the formula derived in step 1: Energy per electron (J) = \(\frac{279.7 \: \text{kJ/mol}}{6.022 \times 10^{23} \: \text{atoms/mol}}\times 1000 \: \text{J/ kJ}\)= \(4.644 \times 10^{-19} \: \text{J}\)
03

Use Planck's equation to find the wavelength of light

Planck's equation relates the energy of a photon with its frequency (v) and wavelength (λ), and is given by: E = h × v = \(\frac{h \times c}{λ}\) Where: E is the energy of the photon (J) h is the Planck's constant, approximately \(6.626 \times 10^{-34} \: \text{J s}\) c is the speed of light, approximately \(3 \times 10^{8} \: \text{m/s}\) λ is the wavelength of light (m) We can rearrange the equation to find the wavelength of light: λ = \(\frac{h \times c}{E}\)
04

Calculate the maximum wavelength of light

Now let's substitute the values we've found into the equation and find the maximum wavelength of light: λ = \(\frac{6.626 \times 10^{-34} \: \text{J s} \times 3 \times 10^{8} \: \text{m/s}}{4.644 \times 10^{-19} \: \text{J}}\) λ = \(4.282 \times 10^{-7}\: \text{m}\) To report the result in nanometers (nm), multiply the result by \(10^9\): λ = \(4.282 \times 10^{-7}\: \text{m} \times 10^9 \: \frac{\text{nm}}{\text{m}}\) λ = 428.2 nm So, the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal is about 428.2 nm.

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Most popular questions from this chapter

Without looking at data in the text, sketch a qualitative graph of the third ionization energy versus atomic number for the elements Na through Ar, and explain your graph.

Which of the following statements is(are) true? a. F has a larger first ionization energy than does Li. b. Cations are larger than their parent atoms. c. The removal of the first electron from a lithium atom (electron configuration is 1\(s^{2} 2 s^{1} )\) is exothermic - that is, removing this electron gives off energy. d. The He atom is larger than the \(\mathrm{H}^{+}\) ion. e. The Al atom is smaller than the Li atom.

In the second row of the periodic table, Be, N, and Ne all have endothermic (unfavorable) electron affinities, whereas the other second-row elements have exothermic (favorable) electron affinities. Rationalize why Be, N, and Ne have unfavorable electron affinities.

In the ground state of cadmium, Cd, a. how many electrons have \(\ell=2\) as one of their quantum numbers? b. how many electrons have \(n=4\) as one of their quantum numbers? c. how many electrons have \(m_{\ell}=-1\) as one of their quantum numbers? d. how many electrons hav \(m_{s}=-\frac{1}{2}\) as one of their quantum numbers?

Answer the following questions assuming that \(m_{s}\) could have three values rather than two and that the rules for \(n, \ell,\) and \(m_{\ell}\) are the normal ones. a. How many electrons would an orbital be able to hold? b. How many elements would the first and second periods in the periodic table contain? c. How many elements would be contained in the first transition metal series? d. How many electrons would the set of 4\(f\) orbitals be able to hold?
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