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Chapter 27: Problem 32

Find the energy for a hydrogen atom in the stationary state \(n=4.\)

Short Answer

Expert verified
Answer: The energy of a hydrogen atom in the stationary state with principal quantum number n = 4 is approximately -0.85 electron-volts.

Step by step solution

01

Recall the energy level formula for a hydrogen atom

The energy level formula for a hydrogen atom is given by: $$E_n = -\frac{13.6\,\text{eV}}{n^2}$$ where \(E_n\) is the energy of the stationary state with quantume number n, and eV represents electron-volt.
02

Plug the given value of n into the energy level formula

We are given that the principal quantum number for the stationary state is n = 4. Plug this value into the energy level formula: $$E_4 = -\frac{13.6\,\text{eV}}{(4)^2}$$
03

Calculate the energy of the hydrogen atom

Now we just have to simplify the expression: $$E_4 = -\frac{13.6\,\text{eV}}{16}$$ $$E_4 = -0.85\,\text{eV}$$ The energy of a hydrogen atom in the stationary state with principal quantum number n = 4 is approximately -0.85 electron-volts.

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Most popular questions from this chapter

Ultraviolet light of wavelength 220 nm illuminates a tungsten surface and electrons are ejected. A stopping potential of \(1.1 \mathrm{V}\) is able to just prevent any of the ejected electrons from reaching the opposite electrode. What is the work function for tungsten?
How much energy must be supplied to a hydrogen atom to cause a transition from the ground state to the \(n=4\) state?
Two different monochromatic light sources, one yellow \((580 \mathrm{nm})\) and one violet \((425 \mathrm{nm}),\) are used in a photoelectric effect experiment. The metal surface has a photoelectric threshold frequency of $6.20 \times 10^{14} \mathrm{Hz}$. (a) Are both sources able to eject photoelectrons from the metal? Explain. (b) How much energy is required to eject an electron from the metal? (Use \(h=4.136 \times\) \(10^{-15} \mathrm{eV} \cdot \mathrm{s} .\)
An FM radio station broadcasts at a frequency of \(89.3 \mathrm{MHz}\). The power radiated from the antenna is \(50.0 \mathrm{kW} .\) (a) What is the energy in electron-volts of each photon radiated by the antenna? (b) How many photons per second does the antenna emit?
The photoelectric effect is studied using a tungsten target. The work function of tungsten is 4.5 eV. The incident photons have energy \(4.8 \mathrm{eV} .\) (a) What is the threshold frequency? (b) What is the stopping potential? (c) Explain why, in classical physics, no threshold frequency is expected.
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