An electron is excited from the n=1 ground state to the n=3...

An electron is excited from the $n=1$ ground state to the $n=3$ state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true. a. It takes more energy to ionize (completely remove) the electron from $n=3$ than from the ground state. b. The electron is farther from the nucleus on average in the $n=3$ state than in the $n=1$ state. c. The wavelength of light emitted if the electron drops from $n=3$ to $n=2$ will be shorter than the wavelength of light emitted if the electron falls from $n=3$ to $n=1$. d. The wavelength of light emitted when the electron returns to the ground state from $n=3$ will be the same as the wavelength of light absorbed to go from $n=1$ to $n=3$. e. For $n=3$, the electron is in the first excited state.

An electron is excited from the $n=1$ ground state to the $n=3$ state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true.
a. It takes more energy to ionize (completely remove) the electron from $n=3$ than from the ground state.
b. The electron is farther from the nucleus on average in the $n=3$ state than in the $n=1$ state.
c. The wavelength of light emitted if the electron drops from $n=3$ to $n=2$ will be shorter than the wavelength of light emitted if the electron falls from $n=3$ to $n=1$.
d. The wavelength of light emitted when the electron returns to the ground state from $n=3$ will be the same as the wavelength of light absorbed to go from $n=1$ to $n=3$.
e. For $n=3$, the electron is in the first excited state.

Key Concepts

Energy Levels

Energy levels in atoms are quantized, meaning electrons can only occupy specific energy states defined by quantum numbers. In the hydrogen atom, these levels are given by distinct principal quantum numbers, with the ground state at n=1 and higher excited states at n>1. This quantization determines many atomic properties including the energy differences required for transitions between states.

Ionization Energy

Ionization energy is the energy required to completely remove an electron from an atom. In the context of quantized energy levels, electrons in lower (more tightly bound) energy states, like the ground state, require more energy to remove than electrons in higher (less tightly bound) states. This principle is critical in understanding atomic behavior and electron binding.

Electron Orbital Radius

The electron orbital radius describes the average distance of an electron from the nucleus. In hydrogen-like atoms, this average distance increases with the principal quantum number. Therefore, electrons in higher energy states are, on average, farther away from the nucleus, impacting both atomic size and the electron’s potential energy.

Photon Emission and Absorption

Photon emission and absorption occur when electrons transition between energy levels. The energy difference between levels corresponds to the energy (and thus the wavelength) of the emitted or absorbed photon. Consequently, transitions involving larger energy differences produce photons with shorter wavelengths, linking photon characteristics with electron dynamics.

Spectral Line Symmetry

Spectral lines in an atom’s emission and absorption spectra can be related by the same energy transition. However, while the energy difference is the same when an electron makes a specific transition, the observed wavelength can differ if the pathway involves intermediate states. Recognizing how these transitions relate is key to understanding atomic spectra.

Excited States

An excited state refers to any state of an atom where an electron has absorbed energy and moved from the ground state to a higher energy level. The designation of first, second, etc., excited states depends on the ordering of energy levels. In a hydrogen atom, the first excited state is the state with the lowest energy above the ground state.

Transcript

0:00 All right, guys.

00:01 You're doing problem 70 of chapter 7.

00:02 So an electron is excited from n equals 1 to the n equals 3 state in hydrogen, which the following statements are true.

00:10 Correct.

00:10 The following statements make them true.

00:12 So it takes more energy to ionize the electron from n equals 3 to then from the ground state, end equals 1.

00:18 That's false.

00:20 It actually takes less energy to completely ionize, take away the n equals 3 electron than an equals 1.

00:28 Because the n equals one electron, that's in a lower energy state.

00:33 That's closer to the nucleus.

00:35 So that's going to have a stronger attraction between your negatively charged electron and your positively charged nucleus.

00:42 If you're further away, that attraction is going to be lessened.

00:47 That's an n consequence that electron will be easier to take off.

00:50 So the electron is farther from nucleus on average in the n equals three state than the n equals one state.

00:55 That's true.

00:57 The higher your end value, the further away from nucleus.

00:59 So the wavelength of light emitted if the electron drops from n equals 3 to n equals 2, we'll be sure then if the wavelength of light emitted if the electron falls from n equals 3 to n equals 1...

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