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Chapter 27: Problem 38

Use the Bohr theory to find the energy necessary to remove the electron from a hydrogen atom initially in its ground state.

Short Answer

Expert verified
Answer: The energy required to remove the electron from a hydrogen atom initially in its ground state is 13.6 electron volts (eV).

Step by step solution

01

Identify given parameters

In this problem, we have a hydrogen atom which means it has only one proton (Z=1) and one electron. Also, the electron is initially in its ground state (n=1).
02

Use Bohr's formula to find the energy of the electron in the ground state

Apply the formula for the energy level of the electron in the hydrogen atom using the given n and Z values: E_n = -13.6 * Z^2 / n^2 eV E_1 = -13.6 * (1)^2 / (1)^2 eV E_1 = -13.6 eV
03

Calculate the energy required to remove the electron

The energy necessary to remove the electron from the hydrogen atom in its ground state is equal to the absolute value of the electron's energy in the ground state: Ionization_energy = |-13.6 eV| Ionization_energy = 13.6 eV So, the energy necessary to remove the electron from the hydrogen atom initially in its ground state is 13.6 electron volts (eV).

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Most popular questions from this chapter

Follow the steps outlined in this problem to estimate the time lag (predicted classically but not observed experimentally) in the photoelectric effect. Let the intensity of the incident radiation be $0.01 \mathrm{W} / \mathrm{m}^{2} .\( (a) If the area of the atom is \)(0.1 \mathrm{nm})^{2},$ find the energy per second falling on the atom. (b) If the work function is 2.0 eV, how long would it take (classically) for enough energy to fall on this area to liberate one photoelectron? (c) Explain briefly, using the photon model, why this time lag is not observed.
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