Chapter 3: Q25E (page 93)

You are an early 20th-century experimental physicist and do not know the value of Planck's constant. By a suitable plot of the following data, and using Einstein's explanation of the photoelectric effect $(KE = W - ϕ$ . where $h$ is not known), determine Planck's constant.

Short Answer

Expert verified

Planck's constant $h = 6.665 \times 10^{- 34} J \cdot s$

Step by step solution

Concept and Formula

Energy $E = hf - ϕ$

Here, $E$ is the energy, $f$ is the frequency and $ϕ$ is the work function.

$E = {eV}_{0}$ . Here, $E$ is the kinetic energy, is the electronic charge and is the stopping potential.

$c = fλ$ Here, $c$ is the speed of light, $f$ is the frequency and $λ$ is the wavelength.

Electronic charge $= 1.602 \times 10^{- 19} C$

Speed of light $= 2.99 \times 10^{8} m \cdot s^{- 1}$ .

Evaluate energy

Energy is given as,

$\begin{matrix} E = hf - ϕ \\ E = {eV}_{0} \\ {eV}_{0} = hf - ϕ \\ V_{0} = \frac{hf}{e} - \frac{ϕ}{e} \end{matrix}$

Substituting $c = fλ$

$\begin{array}{l} V_{0} = \frac{hc}{eλ} - \frac{ϕ}{e} \\ V_{0} = \frac{hc}{e} \times \frac{1}{λ} - \frac{ϕ}{e} \end{array}$

Plot the graph

Plotting a graph of $\frac{1}{λ}$ versus $V_{0}$ using the given data,

Calculate Planck’s constant

From the graph, gradient $= 1244 V \cdot nm$ and intercept $= - 2.2017 V$

As gradient $= \frac{hc}{e}$

$\begin{matrix} 1244 = \frac{hc}{e} \\ h = 1244 \times \frac{e}{r} \end{matrix}$

Substitute values for e and $c$

$\begin{array}{l} h = 1244 V \cdot nm \times \frac{1 .602 \times 10^{- 19} C}{2 .99 \times 10^{8} m \cdot s^{- 1}} \\ h = 1244 \times 10^{- 9} V \cdot m \times \frac{1 .602 \times 10^{- 19} C}{2 .99 \times 10^{8} m \cdot s^{- 1}} \\ h = 6 .665 \times 10^{- 34} J \cdot s \end{array}$

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You are an early 20th-century experimental physicist and do not know the value of Planck's constant. By a suitable plot of the following data, and using Einstein's explanation of the photoelectric effect $(KE = W - ϕ$ . where $h$ is not known), determine Planck's constant.

Short Answer

Step by step solution

Concept and Formula

Evaluate energy

Plot the graph

Calculate Planck’s constant

One App. One Place for Learning.

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You are an early 20th-century experimental physicist and do not know the value of Planck's constant. By a suitable plot of the following data, and using Einstein's explanation of the photoelectric effect (KE=W−ϕ. where his not known), determine Planck's constant.

Short Answer

Step by step solution

Concept and Formula

Evaluate energy

Plot the graph

Calculate Planck’s constant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Rotational Dynamics

Translational Dynamics

Medical Physics

Geometrical and Physical Optics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

You are an early 20th-century experimental physicist and do not know the value of Planck's constant. By a suitable plot of the following data, and using Einstein's explanation of the photoelectric effect $(KE = W - ϕ$ . where $h$ is not known), determine Planck's constant.