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Chapter 7: Problem 68

Assume that a hydrogen atom's electron has been excited to the \(n=5\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

Short Answer

Expert verified
The electron in the hydrogen atom is initially excited to the \(n=5\) energy level and can transition to any of the lower energy levels (\(n=4, 3, 2, 1\)). There are 4 possible transitions (\(5 \rightarrow 4, 5 \rightarrow 3, 5 \rightarrow 2, 5 \rightarrow 1\)), so 4 different wavelengths of light can be emitted as the excited atom loses energy.

Step by step solution

01

Identify the possible transitions for the electron

The electron is initially in the n=5 energy level (also referred to as the 5th shell or principal quantum level). It can transition to any of the lower energy levels (n=4, 3, 2, or 1). Let's list the possible transitions: - 5 to 4 - 5 to 3 - 5 to 2 - 5 to 1
02

Count the number of transitions

Now that we have listed the possible transitions, let's count the number of different energy level transitions that can occur. We have: - One transition from 5 to 4 - One transition from 5 to 3 - One transition from 5 to 2 - One transition from 5 to 1 This gives us a total of 4 distinct energy level transitions.
03

Determine the number of wavelengths emitted as the atom loses energy

Since there are 4 distinct energy level transitions, the hydrogen atom can emit 4 different wavelengths of light as it loses energy. And remember, each of these transitions corresponds to a specific wavelength of light. So, the answer is 4 different wavelengths of light can be emitted as the excited hydrogen atom loses energy.

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Most popular questions from this chapter

Give a possible set of values of the four quantum numbers for all the electrons in a boron atom and a nitrogen atom if each is in the ground state.

One of the emission spectral lines for \(\mathrm{Be}^{3+}\) has a wavelength of 253.4 \(\mathrm{nm}\) for an electronic transition that begins in the state with \(n=5 .\) What is the principal quantum number of the lower-energy state corresponding to this emission? (Hint: The Bohr model can be applied to one- electron ions. Don't forget the \(Z\) factor: \(Z=\) nuclear charge \(=\) atomic number.)

An unknown element is a nonmetal and has a valence electron configuration of \(n s^{2} n p^{4} .\) a. How many valence electrons does this element have? b. What are some possible identities for this element? c. What is the formula of the compound this element would form with potassium? d. Would this element have a larger or smaller radius than barium? e. Would this element have a greater or smaller ionization energy than fluorine?

Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at 1.00\(\%\) of the speed of light. b. Calculate the velocity of a neutron with a wavelength of 75 \(\mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{m}\right)\)

The successive ionization energies for an unknown element are $$\begin{aligned} I_{1} &=896 \mathrm{kJ} / \mathrm{mol} \\ I_{2} &=1752 \mathrm{kJ} / \mathrm{mol} \\ I_{3} &=14,807 \mathrm{kJ} / \mathrm{mol} \\\ I_{4} &=17,948 \mathrm{kJ} / \mathrm{mol} \end{aligned}$$ To which family in the periodic table does the unknown element most likely belong?
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