Q: Using Bohr's equation $$E_n = -2.18 \times 10$$^{-18}$$ \ \mathrm{J} \left( \dfrac{1}{n^2$} \right)$$, what is the energy difference when an electron transitions from $$n=3 to$$ $$n=2$$?

$$3.03 \times 10$$^{-19}$$ \ \mathrm{J}$$

Q: A baseball of mass $$0.2 \ \mathrm{kg}$$ travels at $$36 \ \mathrm{m/s}. $$Calculate its de Broglie wavelength using $$h = 6.626 \times 10$$^{-34}$$ \ \mathrm{J \cdot s}.$$

$$9.2 \times 10$$^{-35}$$ \ \mathrm{m}$$

Q: An electron has a speed of $$6 \times 10^6$ \ \mathrm{m/s}$$ with an uncertainty of $$2\%. $$What is the uncertainty in its position? ($$h = 6.626 \times 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$m_e = 9.11 \times 10$$^{-31}$$ \ \mathrm{kg})$$

$$1.5 \times 10$$^{-9}$$ \ \mathrm{m}$$

Question 1

Which equation correctly relates the wavelength $$\lambda$$ and frequency $$
u of $$electromagnetic waves, where $$c is $$the speed of light?

Accepted Answer

$$c = \lambda 
u$$

Question 2

According to Planck's model of blackbody radiation, energy is emitted in discrete packets. What is the equation for the energy $$E of a $$photon with frequency $$
u$$?

Accepted Answer

$$E = h 
u$$

Question 3

Einstein explained the photoelectric effect by proposing that light consists of photons. Which statement best describes the energy of a photon?

Accepted Answer

It is proportional to the frequency of light.

Question 4

The Rydberg-Balmer equation describes the hydrogen atom's line spectrum. Which equation represents the relationship between the wavelengths of emitted light and quantum numbers $$n_1$$ and $$n_2$$?

Accepted Answer

$$\dfrac{1}{\lambda} = R_\infty \left( \dfrac{1}{n_1$^2} - \dfrac{1}{n_2$^2} \right)$$

Question 5

Which of the following is NOT a postulate of the Bohr model of the hydrogen atom?

Accepted Answer

Electrons radiate energy continuously while in a quantum level.

Question 6

Using Bohr's equation $$E_n = -2.18 	imes 10$$^{-18}$$ \ \mathrm{J} \left( \dfrac{1}{n^2$} ight)$$, what is the energy difference when an electron transitions from $$n=3 to$$ $$n=2$$?

Accepted Answer

$$3.03 	imes 10$$^{-19}$$ \ \mathrm{J}$$

Question 7

Why does the Bohr model fail for atoms with more than one electron?

Accepted Answer

It cannot account for electron-electron repulsion.

Question 8

De Broglie proposed that matter has wave-like properties. What is the equation for the de Broglie wavelength $$\lambda of an $$object with mass $$m$$ and speed $$u$$?

Accepted Answer

$$\lambda = h / (m u)$$

Question 9

A baseball of mass $$0.2 \ \mathrm{kg}$$ travels at $$36 \ \mathrm{m/s}. $$Calculate its de Broglie wavelength using $$h = 6.626 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s}.$$

Accepted Answer

$$9.2 	imes 10$$^{-35}$$ \ \mathrm{m}$$

Question 10

Which statement best explains why the de Broglie wavelength is significant for electrons but not for everyday objects?

Accepted Answer

Electrons have much smaller mass, resulting in a larger wavelength.

Question 11

Which equation expresses the Heisenberg uncertainty principle for position $$\Delta x$$ and momentum $$m \Delta u$$?

Accepted Answer

$$\Delta x \cdot m \Delta u \geq \dfrac{h}{4 \pi}$$

Question 12

An electron has a speed of $$6 	imes 10^6$ \ \mathrm{m/s}$$ with an uncertainty of $$2\%. $$What is the uncertainty in its position? ($$h = 6.626 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$m_e = 9.11 	imes 10$$^{-31}$$ \ \mathrm{kg})$$

Accepted Answer

$$1.5 	imes 10$$^{-9}$$ \ \mathrm{m}$$

Question 13

Which of the following statements about the Heisenberg uncertainty principle is correct?

Accepted Answer

It is only important for objects with very small mass.

Question 14

Schrodinger's equation describes the behavior of electrons in atoms. What is the physical meaning of the square of the wavefunction $$|\psi|^2$$?

Accepted Answer

It gives the probability of finding the electron at a particular point in space.

Question 15

Which concept best describes the dual nature of matter and energy, as shown by experiments with electrons and photons?

Accepted Answer

Wave-particle duality

Question 16

A hydrogen atom emits light as an electron falls from $$n=3 to$$ $$n=1. $$Which statement is true about the energy and wavelength of the emitted photon?

Accepted Answer

The photon has higher energy and shorter wavelength than a transition from $$n=2 to$$ $$n=1.$$

Question 17

Which real-world demonstration illustrates atomic line spectra and the quantization of energy levels?

Accepted Answer

A sodium vapor lamp emitting yellow light

Question 18

Which statement about atomic orbitals (wavefunctions) is correct?

Accepted Answer

Each atomic orbital corresponds to a specific energy state of the atom.

Atomic Line Spectra, Bohr Model, Quantum Mechanics, and the Uncertainty Principle

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