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Chapter 2: Problem 51

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 that can provide enough energy to remove an electron from an iron atom is 275 nm.

Step by step solution

01

Write down the given values and the Planck-Einstein relation equation

We are given the energy E needed to remove an electron, which is \(7.21 \times 10^{-19} \mathrm{J}\). We'll also need the values for the Planck constant h (\(6.63 \times 10^{-34} \mathrm{Js}\)) and the speed of light c (\(3.00 \times 10^8 \frac{\mathrm{m}}{\mathrm{s}}\)). We want to find the wavelength λ. The Planck-Einstein relation is: \[E = \dfrac{hc}{\lambda}\]
02

Rearrange the equation to solve for the wavelength λ

We want to find the value of λ. To do this, we need to rearrange the equation so that it is in the form λ =... . We can do this by multiplying both sides of the equation by λ and then dividing by E. This gives: \[\lambda = \dfrac{hc}{E}\]
03

Substitute the known values and find the maximum wavelength

Now we can substitute the given values for h, c, and E into the equation: \[\lambda = \dfrac{(6.63 \times 10^{-34} \mathrm{Js})(3.00 \times 10^8 \frac{\mathrm{m}}{\mathrm{s}})}{7.21 \times 10^{-19} \mathrm{J}}\] Perform the calculation to find the value of λ: \[\lambda = \dfrac{(6.63 \times 10^{-34})(3.00 \times 10^8)}{7.21 \times 10^{-19}} \approx 2.75 \times 10^{-7} \mathrm{m}\] Since we usually express wavelength in nanometers (nm), we can convert the result by multiplying by \(10^9\): \[\lambda = 2.75 \times 10^{-7} \mathrm{m} \times 10^9 \frac{\mathrm{nm}}{\mathrm{m}} = 275 \mathrm{nm}\]
04

State the final answer

The maximum wavelength of light that can provide enough energy to remove an electron from an iron atom is 275 nm.

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Most popular questions from this chapter

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