Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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**Photoelectric Effect and Work Function Calculation**

Iron has a work function (Φ) of 4.50 eV. What is the longest wavelength of light, in nanometers (nm), that will cause the ejection of electrons? Given: 1 eV = 1.6 × 10⁻¹⁹ J.

**Explanation:**

The work function is the minimum energy required to eject an electron from the surface of a material. To find the longest wavelength (λ) of light that can achieve this, we can use the equation:

\[ E = \frac{hc}{λ} \]

Where:
- \( E \) is the energy in joules,
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( c \) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).

Convert the work function from eV to joules:
\[ E = 4.50 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} \]

Plug this energy value into the equation to find the wavelength:
\[ λ = \frac{hc}{E} \]

Calculate to find the longest wavelength that can cause the ejection of electrons.
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Transcribed Image Text:**Photoelectric Effect and Work Function Calculation** Iron has a work function (Φ) of 4.50 eV. What is the longest wavelength of light, in nanometers (nm), that will cause the ejection of electrons? Given: 1 eV = 1.6 × 10⁻¹⁹ J. **Explanation:** The work function is the minimum energy required to eject an electron from the surface of a material. To find the longest wavelength (λ) of light that can achieve this, we can use the equation: \[ E = \frac{hc}{λ} \] Where: - \( E \) is the energy in joules, - \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)), - \( c \) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)). Convert the work function from eV to joules: \[ E = 4.50 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} \] Plug this energy value into the equation to find the wavelength: \[ λ = \frac{hc}{E} \] Calculate to find the longest wavelength that can cause the ejection of electrons.
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