Q: Which equation correctly describes the energy change ($$\Delta E) $$for an electron transition in the hydrogen atom according to the Bohr model?

$$\Delta E = -13.6 \text{ eV} \left( \dfrac{1}{n_f^2$} - \dfrac{1}{n_i^2$} \right)$$

Question 1

Which equation correctly describes the energy change ($$\Delta E) $$for an electron transition in the hydrogen atom according to the Bohr model?

Accepted Answer

$$\Delta E = -13.6 	ext{ eV} \left( \dfrac{1}{n_f^2$} - \dfrac{1}{n_i^2$} ight)$$

Question 2

An electron in a hydrogen atom transitions from $$n=4 to$$ $$n=2. $$Which of the following best describes the type of light emitted?

Accepted Answer

Visible light

Question 3

Given the wavelength range of visible light is 400–700 nm, which transition in hydrogen is most likely to produce visible light?

Accepted Answer

$$n=3 \rightarrow n=2$$

Question 4

Calculate the energy released when an electron in hydrogen transitions from $$n=3 to$$ $$n=2. $$Use $$E_n = -13.6 	ext{ eV}/n^2$.

Accepted Answer

$$1.89 	ext{ eV}$$

Question 5

Which formula should be used to calculate the wavelength ($$\lambda) of $$light emitted during an electron transition in hydrogen?

Accepted Answer

$$\lambda = \dfrac{hc}{|\Delta E|}$$

Question 6

A student observes a bright-line spectrum for an unknown element. What does each line in the spectrum represent?

Accepted Answer

A specific electron transition between energy levels

Question 7

If a transition in hydrogen emits a photon with a wavelength of 656 nm, which series does this belong to?

Accepted Answer

Balmer series

Question 8

Which transition in the hydrogen atom emits the highest energy photon?

Accepted Answer

$$n=2 \rightarrow n=1$$

Question 9

A sample emits spectral lines at the same wavelengths as element A and element B. What can you conclude about the sample?

Accepted Answer

The sample contains both element A and element B

Question 10

Why do different elements produce unique bright-line spectra?

Accepted Answer

Each element has a unique set of energy levels

Question 11

Which of the following best explains why the $$n=2 \rightarrow n=1$$ transition in hydrogen does not produce visible light?

Accepted Answer

The energy released is too high, resulting in ultraviolet light

Question 12

A scientist uses a spectroscope to analyze a star and finds lines matching hydrogen's Balmer series. What does this indicate?

Accepted Answer

Hydrogen is present in the star

Question 13

Which transition in hydrogen would produce a photon with the shortest wavelength?

Accepted Answer

$$n=5 \rightarrow n=1$$

Question 14

If the energy difference between two levels in hydrogen is $$2.55 	ext{ eV}$$, what is the wavelength of the emitted photon? ($$h = 4.1357 	imes 10$$^{-15}$$ 	ext{ eV} \cdot 	ext{s}$$, $$c = 3.00 	imes 10^8$ 	ext{ m/s})$$

Accepted Answer

$$487 	ext{ nm}$$

Question 15

Which of the following is NOT a reason why the Bohr model is limited in explaining atomic spectra?

Accepted Answer

It accurately predicts all atomic spectra

Question 16

A hospital uses emission spectra to identify elements in a blood sample. What property of atoms allows this technique to work?

Accepted Answer

Atoms emit photons at specific wavelengths during electron transitions

Question 17

Which transition in hydrogen would produce a photon in the infrared region?

Accepted Answer

$$n=4 \rightarrow n=3$$

Question 18

If an unknown sample shows spectral lines at 486 nm and 656 nm, which element is most likely present?

Accepted Answer

Hydrogen

Question 19

Which of the following best describes the relationship between electron transitions and the color of light emitted?

Accepted Answer

The energy difference between levels determines the wavelength and color

Bohr Model of Hydrogen and Atomic Spectra: Study Notes

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