Chapter 7, Problem 7.84P

(a)

Interpretation Introduction

Interpretation:

The kinetic energy of the electron dislodged from the potassium surface is to be determined.

Concept introduction:

The major points of the Einstein photoelectric effect are as follows:

1) Light consists of photons. Each photon has an energy equivalent to $h\nu$.

2) The collision of a photon and an electron on the metal surface is elastic in nature.

3) Out of the total energy gained by the electron, some of it is used by the electron to lodge out of the metal surface whereas the remaining part is the kinetic energy of the electron.

4) The minimum energy required to lodge an electron out of the metal surface is called the work function of the metal.

5) The remaining energy is the maximum kinetic energy of the photoelectron.

(b)

Interpretation Introduction

Interpretation:

The work function of potassium is to be determined.

Concept introduction:

The major points of the Einstein photoelectric effect are as follows:

1) Light consists of photons. Each photon has an energy equivalent to $h\nu$.

2) The collision of a photon and an electron on the metal surface is elastic in nature.

3) Out of the total energy gained by the electron, some of it is used by the electron to lodge out of the metal surface whereas the remaining part is the kinetic energy of the electron.

4) The minimum energy required to lodge an electron out of the metal surface is called the work function of the metal.

5) The remaining energy is the maximum kinetic energy of the photoelectron.

Energy is proportional to the frequency and is expressed by the Plank-Einstein equation as follows:

$E=h\nu$ (2)

Here,

$E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency.

The equation to relate the frequency and wavelength of electromagnetic radiation is as follows:

$\nu =\frac{c}{\lambda }$

Equation (2) can be modified as,

$E=h\left(\frac{c}{\lambda }\right)$ (3)

Here,

$c$ is the speed of light.

$\lambda$ is the wavelength.

The conversion factor to convert wavelength from $\text{nm}$ to $\text{m}$ is,

$1\text{ nm}=1\times {10}^{-9}\text{ m}$