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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

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.
(a) Light of wavelength 300 nm is incident on a metal that has a work function of 1.4 eV. What is the maximum speed of the emitted electrons? (b) Repeat part (a) for light of wavelength 800 nm incident on a metal that has a work function of \(1.6 \mathrm{eV} .\) (c) How would your answers to parts (a) and (b) vary if the light intensity were doubled?
A hydrogen atom in its ground state is immersed in a continuous spectrum of ultraviolet light with wavelengths ranging from 96 nm to 110 nm. After absorbing a photon, the atom emits one or more photons to return to the ground state. (a) What wavelength(s) can be absorbed by the \(\mathrm{H}\) atom? (b) For each of the possibilities in (a), if the atom is at rest before absorbing the UV photon, what is its recoil speed after absorption (but before emitting any photons)? (c) For each of the possibilities in (a), how many different ways are there for the atom to return to the ground state?
A clean iron surface is illuminated by ultraviolet light. No photoelectrons are ejected until the wavelength of the incident UV light falls below 288 nm. (a) What is the work function (in electron-volts) of the metal? (b) What is the maximum kinetic energy for electrons ejected by incident light of wavelength \(140 \mathrm{nm} ?\)
An incident photon of wavelength \(0.0100 \mathrm{nm}\) is Compton scattered; the scattered photon has a wavelength of \(0.0124 \mathrm{nm} .\) What is the change in kinetic energy of the electron that scattered the photon?
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