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Chapter 38: Problem 8

An electron made a transition between allowed states emitting a photon. What physical constants are needed to calculate the energy of photon from the measured wavelength? (select all that apply) a) the Plank constant, \(h\) b) the basic electric charge, \(e\) c) the speed of light in vacuum, \(c\) d) the Stefan-Boltzmann constant, \(\sigma\)

Short Answer

Expert verified
Answer: a) the Planck constant (h), c) the speed of light in vacuum (c)

Step by step solution

01

1. Identify the energy-wavelength relationship for a photon

The energy of a photon (E) can be found using the following equation: E = h * c / λ, where: - E is the energy of the photon, - h is the Planck constant, - c is the speed of light in vacuum, and - λ is the wavelength of the photon.
02

2. Analyze the equation for required constants

From the energy-wavelength relationship, we can see that only two physical constants are involved in the calculation: - The Planck constant (h) - The speed of light in vacuum (c)
03

3. Conclusion

The physical constants needed to calculate the energy of the photon from the measured wavelength are: a) the Planck constant, \(h\) c) the speed of light in vacuum, \(c\) The other given constants, the basic electric charge (e) and the Stefan-Boltzmann constant (σ), are not required for this calculation.

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Most popular questions from this chapter

Electrons with the same value of quantum number \(n\) are said to occupy the same electron shell \(K, L, M, N,\) etc. Calculate the maximum allowed number of electrons for the a) \(K\) shell, b) \(L\) shell, and c) \(M\) shell.

A low-power laser has a power of \(0.50 \mathrm{~mW}\) and a beam diameter of \(3.0 \mathrm{~mm}\). a) Calculate the average light intensity of the laser beam, and b) compare it to the intensity of a 100 -W light bulb producing light viewed from \(2.0 \mathrm{~m}\).

A ruby laser consists mostly of alumina \(\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)\) and a small amount of chromium ions, responsible for its red color. One such laser of power \(3.00 \mathrm{~kW}\) emits light pulse of duration \(10.0 \mathrm{~ns}\) and of wavelength \(685 \mathrm{nm}\). a) What is the energy of the photons in the pulse? b) Determine the number of chromium atoms undergoing stimulated emission to produce this pulse.

The radial wave function for hydrogen in the \(1 s\) state is given by \(R_{1 s}=A_{1} e^{-r / a_{0}}\) a) Calculate the normalization constant \(A_{1}\). b) Calculate the probability density at \(r=a_{0} / 2\). c) The \(1 s\) wave function has a maximum at \(r=0\) but the \(1 s\) radial density peaks at \(r=a_{0} .\) Explain this difference.

The wavelength of the fourth line in the Lyman series is a) \(80.0 \mathrm{nm}\). b) \(85.0 \mathrm{nm}\). c) \(90.2 \mathrm{nm}\). d) \(94.9 \mathrm{nm}\).
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