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Chapter 2: Problem 150

It takes \(476 \mathrm{kJ}\) to remove 1 mole of electrons from the atoms at the surface of a solid metal. How much energy (in kJ) does it take to remove a single electron from an atom at the surface of this solid metal?

Short Answer

Expert verified
The energy required to remove a single electron from an atom at the surface of this solid metal is \(7.910 \times 10^{-22}\, kJ\).

Step by step solution

01

Identify known values and conversion factor

\ We know the following: 1. Energy to remove 1 mole of electrons: \(476 kJ\) 2. Conversion factor: Avogadro's number \(N_A = 6.022 \times 10^{23} \, \mathrm{mol}^{-1}\) We need to find the energy required to remove a single electron.
02

Use the conversion factor to find the energy required for a single electron

\ To calculate the energy required to remove one electron, we will divide the given energy for 1 mole of electrons (476 kJ) by the Avogadro's number. Energy per electron = \(\frac{Energy \, for \, 1 \, mol}{Avogadro's \, number}\) Energy per electron = \(\frac{476\, kJ}{6.022 \times 10^{23}\, \mathrm{electron\cdot mol^{-1}}}\)
03

Calculate the energy required for a single electron

\ Now, perform the calculation: Energy per electron = \(\frac{476 \times 10^3\, J}{6.022 \times 10^{23}\, electrons}\) Energy per electron = \(7.910 \times 10^{-19}\, J\)
04

Convert Joules to Kilojoules

\ To express the result in kJ, we need to convert Joules to Kilojoules by dividing the value by \(10^3\). Energy per electron = \(\frac{7.910 \times 10^{-19}\, J}{10^3\frac{J}{kJ}}\) Energy per electron = \(7.910 \times 10^{-22}\, kJ\)
05

Write the final answer

\ The energy required to remove a single electron from an atom at the surface of this solid metal is \(7.910 \times 10^{-22}\, kJ\).

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Most popular questions from this chapter

For each of the following pairs of elements $$(\mathrm{Mg} \text { and } \mathrm{K}) \quad(\mathrm{F} \text { and } \mathrm{Cl})$$ pick the atom with a. more favorable (more negative) electron affinity. b. higher ionization energy. c. larger size.

The first-row transition metals from chromium through zinc all have some biologic function in the human body. How many unpaired electrons are present in each of these first-row transition metals in the ground state?

The successive ionization energies for an unknown element are \(I_{1}=896 \mathrm{kJ} / \mathrm{mol}\) \(\overline{I_{2}}=1752 \mathrm{kJ} / \mathrm{mol}\) \(I_{3}=14,807 \mathrm{kJ} / \mathrm{mol}\) \(I_{4}=17,948 \mathrm{kJ} / \mathrm{mol}\) To which family in the periodic table does the unknown element most likely belong?

In each of the following sets, which atom or ion has the smallest ionization energy? a. \(\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}\) b. \(\mathrm{K}, \mathrm{Mn}, \mathrm{Ga}\) c. \(\mathrm{N}, \mathrm{O}, \mathrm{F}\) d. \(S^{2-}, S, S^{2+}\) e. \(\mathrm{Cs}, \mathrm{Ge}, \mathrm{Ar}\)

The wave function for the \(2 p_{z}\) orbital in the hydrogen atom is $$ \psi_{2 p_{i}}=\frac{1}{4 \sqrt{2 \pi}}\left(\frac{Z}{a_{0}}\right)^{3 / 2} \sigma \mathrm{e}^{-\alpha / 2} \cos \theta $$ where \(a_{0}\) is the value for the radius of the first Bohr orbit in meters \(\left(5.29 \times 10^{-11}\right), \sigma\) is \(Z\left(r / a_{0}\right), r\) is the value for the distance from the nucleus in meters, and \(\theta\) is an angle. Calculate the value of \(\psi_{2 p^{2}}\) at \(r=a_{0}\) for \(\theta=0^{\circ}\left(z \text { axis) and for } \theta=90^{\circ}\right.\) (xy plane).
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