Question

Photoelectrons with a maximum speed of 7.00 × 10⁶ m/s are ejected from a surface in the presence of light with a frequency of 8.00 × 10¹4 Hz. If the mass of an electron is 9.10 × 10⁻31 kg, calculate in joules the maximum kinetic energy of a single electron.

A) 4.04 × 10⁻18 J
B) 3.82 × 10⁻18 J
C) 5.61 × 10⁻18 J
D) 6.73 × 10⁻18 J

Answer 1

The maximum kinetic energy of a single electron can be calculated using the equation KE = hf - BE, where hf is the photon energy and BE is the binding energy of the electron in the material. Given the frequency and maximum speed, we can find the photon energy and subtract the binding energy to find the maximum kinetic energy of a single electron.

Step-by-step explanation:

The maximum kinetic energy (KE) of a single electron can be calculated using the equation KE = hf - BE, where hf is the photon energy and BE is the binding energy of the electron in the material. Given a frequency of 8.00 × 10^14 Hz and a maximum speed of 7.00 × 10^6 m/s, we can find the photon energy:

1. First, convert the frequency from Hz to Joules using the formula hf = E_photon, where h is Planck's constant (6.626 × 10^-34 J*s). So, E_photon = 8.00 × 10^14 Hz × 6.626 × 10^-34 J*s = 5.301 × 10^-19 J.
2. Then, subtract the binding energy of the electron, which is given as 4.73 eV. Convert the binding energy from eV to Joules using the conversion factor 1 eV = 1.602 × 10^-19 J. So, BE = 4.73 eV × 1.602 × 10^-19 J/eV = 7.58 × 10^-19 J.

Finally, subtract the binding energy from the photon energy to find the maximum kinetic energy:

KE = E_photon - BE = 5.301 × 10^-19 J - 7.58 × 10^-19 J = -2.279 × 10^-19 J.

Since kinetic energy cannot be negative, the maximum kinetic energy of a single electron is 2.279 × 10^-19 J when ejected from the surface.