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Chapter 6: Problem 64

What is the longest wavelength of radiation that can eject a photoelectron from potassium, given the work function of potassium 2.24 eV? Is it in the visible range?

Short Answer

Expert verified
The longest wavelength of radiation that can eject a photoelectron from potassium is 554 nm, which falls within the visible range (approximately 400 nm to 700 nm).

Step by step solution

01

Write down the formula for energy of a photon

To find the energy of a photon, we use the formula: \(E = h \cdot f\), where \(E\) is the energy in Joules, \(h\) is the Planck constant (\(6.63 \times 10^{-34} \ Js\)), and \(f\) is the frequency in Hz.
02

Convert the work function to Joules

We are given the work function of potassium in electron volts (eV) which is 2.24 eV. We need to convert it to Joules using the conversion factor: \(1 eV = 1.6 \times 10^{-19} J\). So, work function in Joules will be: \(2.24 eV \cdot 1.6 \times 10^{-19} J/eV = 3.584 \times 10^{-19} J\)
03

Calculate the frequency using the energy and Planck constant

Now we can find the frequency using the formula \(E = h \cdot f\). Rearranging the formula to solve for \(f\), we have: \(f = \frac{E}{h} = \frac{3.584 \times 10^{-19} J}{6.63 \times 10^{-34} Js} = 5.41 \times 10^{14} Hz\)
04

Convert frequency to wavelength

To find the wavelength, we use the formula \(c = \lambda \cdot f\), where \(c\) is the speed of light (\(3 \times 10^8 m/s\)), \(f\) is the frequency, and \(λ\) is the wavelength. Rearranging the formula to solve for \(λ\), we have: \(λ_{max} = \frac{c}{f} = \frac{3 \times 10^8 m/s}{5.41 \times 10^{14} Hz} = 5.54 \times 10^{-7} m = 554 nm\)
05

Check if the wavelength is in the visible range

The visible range of light is approximately from 400 nm to 700 nm. Since the wavelength we calculated is 554 nm, it falls within the visible range. Therefore, the longest wavelength of radiation that can eject a photoelectron from potassium is 554 nm, and it is in the visible range.

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Most popular questions from this chapter

What is the longest wavelength that light can have if it is to be capable of ionizing the hydrogen atom in its ground state?

A 600-nm light falls on a photoelectric surface and electrons with the maximum kinetic energy of \(0.17 \mathrm{eV}\) are emitted. Determine (a) the work function and (b) the cutoff frequency of the surface. (c) What is the stopping potential when the surface is illuminated with light of wavelength \(400 \mathrm{nm} ?\)

(a) For what temperature is the peak of blackbody radiation spectrum at \(400 \mathrm{nm} ?\) (b) If the temperature of a blackbody is \(800 \mathrm{K},\) at what wavelength does it radiate the most energy?

Which type of radiation is most suitable for the observation of diffraction patterns on crystalline solids; radio waves, visible light, or X-rays? Explain.

Experiments are performed with ultracold neutrons having velocities as small as \(1.00 \mathrm{m} / \mathrm{s}\). Find the wavelength of such an ultracold neutron and its kinetic energy.
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