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Chapter 7: Problem 56

It takes 208.4 kJ of energy to remove 1 mole of electrons from an atom on the surface of rubidium metal. How much energy does it take to remove a single electron from an atom on the surface of solid rubidium? What is the maximum wavelength of light capable of doing this?

Short Answer

Expert verified
The energy required to remove a single electron from an atom on the surface of solid rubidium is \(3.46 \times 10^{-19} \) J/electron. The maximum wavelength of light capable of doing this is 572 nm.

Step by step solution

01

Convert energy from moles to single electron

To find the energy required to remove one electron from an atom on the surface of solid rubidium, we can use the following conversion: Energy per single electron (J/electron) = Energy per mole (J/mole) / Avogadro's number (electrons/mole) Given: Energy per mole = 208.4 kJ/mole = 208400 J/mole (convert from kJ to J) Avogadro's number = 6.022 x 10^23 electrons/mole So, Energy per single electron = \( \frac{208400}{6.022 \times 10^{23}} \) J/electron
02

Calculate energy per single electron

We can now calculate the energy by inserting the given values: Energy per single electron = \( \frac{208400}{6.022 \times 10^{23}} = 3.46 \times 10^{-19} \) J/electron
03

Use Planck's equation to determine maximum wavelength

Next, we want to find the maximum wavelength of light capable of removing one electron from the atom. To do this, we'll use Planck's equation relating energy (E), wavelength (\( \lambda \)), and Planck's constant (h). \( E = \frac{hc}{\lambda} \) Where: E = 3.46 x 10^(-19) J/electron (from step 2) h = 6.626 x 10^(-34) Js (Planck's constant) c = 3.0 x 10^8 m/s (speed of light) We need to solve for λ: \( \lambda = \frac{hc}{E} \)
04

Calculate maximum wavelength

By inserting the values, we can find the maximum wavelength: \( \lambda = \frac{(6.626 \times 10^{-34})(3.0 \times 10^8)}{3.46 \times 10^{-19}} = 5.72 \times 10^{-7} \) m Now, let's convert this value to nanometers for a more convenient unit: \( \lambda = 5.72 \times 10^{-7} \times 10^9 = 572 \) nm So, the maximum wavelength of light capable of removing one electron from an atom on the surface of solid rubidium is 572 nm.

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Most popular questions from this chapter

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. \(n=4 \rightarrow n=3\) b. \(n=5 \rightarrow n=4\) c. \(n=5 \rightarrow n=3\)

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?

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