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Chapter 27: Problem 7

The minimum energy required to remove an electron from a metal is 2.60 eV. What is the longest wavelength photon that can eject an electron from this metal?

Short Answer

Expert verified
Answer: The longest wavelength of a photon that can eject an electron from the metal is 477 nm.

Step by step solution

01

Convert energy from eV to joules

Given the minimum energy required to remove an electron from the metal is 2.60 eV. We need to convert this energy into joules (J) to use it in our formula. To do this, we will use the conversion factor: 1 eV = 1.6 x 10^-19 J. So, E = 2.60 eV × (1.6 x 10^-19 J/eV) = 4.16 x 10^-19 J
02

Rearrange the equation to solve for wavelength

The relationship between the energy of a photon and its wavelength is given by E = (hc)/λ. We want to solve for the wavelength, so we will rearrange the equation as follows: λ = (hc)/E
03

Plug in the values and calculate the wavelength

Now, we will plug in the values for Planck's constant (h), the speed of light (c), and the energy (E) and calculate the wavelength (λ): λ = (6.626 x 10^-34 J·s × 3.00 x 10^8 m/s) / (4.16 x 10^-19 J) = 4.77 x 10^-7 m
04

Convert the wavelength to nanometers

The calculated wavelength is in meters, but it is often more convenient to express wavelengths in nanometers (nm). To convert from meters to nanometers, we will use the conversion factor: 1 m = 10^9 nm. So, λ = 4.77 x 10^-7 m × (10^9 nm/m) = 477 nm The longest wavelength photon that can eject an electron from this metal is 477 nm.

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