Q: According to de Broglie's hypothesis, what is the wavelength of an electron with mass $$9.11 \times 10$$^{-31}$$ kg moving at 2.00$$ \times $$10^6 m/s$$? (Planck's constant $$h = 6.63 \times 10$$^{-34}$$ J·s)

$$\lambda = \frac{h}{mv} = \frac{6.63 \times 10$$^{-34}$$}{9.11 \times 10$$^{-31}$$ \times 2.00 \times 10^6$} = 3.64 \times 10$$^{-10}$$ m

Question 1

According to the Bohr model, which of the following statements about the energy of an electron in a hydrogen atom is correct?

Accepted Answer

The energy of the electron is quantized and only certain discrete energy levels are allowed.

Question 2

Which equation correctly represents the energy of an electron in the nth orbit of a hydrogen atom according to the Bohr model?

Accepted Answer

$$E_n = -R_H \left( \frac{1}{n^2$} \right)$$

Question 3

A hydrogen atom's electron transitions from $$n=5 to$$ $$n=3. $$Which type of electromagnetic radiation is emitted?

Accepted Answer

Infrared

Question 4

Which of the following best explains why the Bohr model fails for atoms with more than one electron?

Accepted Answer

It does not consider electron-electron repulsions and fails to explain the quantization of energy for multi-electron atoms.

Question 5

According to de Broglie's hypothesis, what is the wavelength of an electron with mass $$9.11 	imes 10$$^{-31}$$ kg moving at 2.00$$ 	imes $$10^6 m/s$$? (Planck's constant $$h = 6.63 	imes 10$$^{-34}$$ J·s)

Accepted Answer

$$\lambda = \frac{h}{mv} = \frac{6.63 	imes 10$$^{-34}$$}{9.11 	imes 10$$^{-31}$$ 	imes 2.00 	imes 10^6$} = 3.64 	imes 10$$^{-10}$$ m

Question 6

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($$l)$$

Question 7

How many possible values of the magnetic quantum number $$m_l$$ are there for a $$d$$ orbital?

Accepted Answer

5

Question 8

Which of the following statements about $$s$$ orbitals is correct?

Accepted Answer

$$s$$ orbitals are spherical in shape and have $$l=0.$$

Question 9

An electron in a hydrogen atom absorbs a photon and moves from $$n=2 to$$ $$n=4. $$Which of the following is true?

Accepted Answer

The electron absorbs energy and moves to a higher energy state.

Question 10

Which of the following best describes the Heisenberg uncertainty principle?

Accepted Answer

The more precisely the position of a particle is known, the less precisely its momentum can be known.

Question 11

How many orbitals are present in the $$n=3$$ energy level of an atom?

Accepted Answer

9

Question 12

Which set of quantum numbers is not allowed for an electron in an atom?

Accepted Answer

$$n=2,\ l=2,\ m_l=0$$

Question 13

Which of the following transitions in a hydrogen atom would result in the emission of the highest energy photon?

Accepted Answer

$$n=2 to$$ $$n=1$$

Question 14

What is the total number of $$f$$ orbitals in a given energy level?

Accepted Answer

7

Question 15

Which quantum number(s) determine the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number ($$m_l) $$only

Question 16

A photon with energy $$E is $$emitted when an electron transitions from $$n_i to$$ $$n_f in a $$hydrogen atom. Which equation correctly relates the energy of the photon to the initial and final energy levels?

Accepted Answer

$$E = -R_H \left( \frac{1}{n_f^2$} - \frac{1}{n_i^2$} \right)$$

Question 17

Which of the following best describes the difference between an orbital and an orbit?

Accepted Answer

An orbit is a fixed circular path as described by Bohr, while an orbital is a region of space described by quantum mechanics where the probability of finding an electron is high.

Question 18

Which of the following is a limitation of the Bohr model?

Accepted Answer

It does not explain why only certain orbits are allowed for electrons.

Question 19

Which of the following statements about $$p$$ orbitals is correct?

Accepted Answer

$$p$$ orbitals have two lobes with a node between them and $$l=1.$$

Question 20

A student claims that the quantum numbers $$n=3$$, $$l=2$$, $$m_l=3$$ are valid for an electron in an atom. Is this correct?

Accepted Answer

No, because $$m_l$$ must be between $$-l$$ and $$+l ($$including zero), so $$m_l=3 is $$not allowed for $$l=2.$$

Electronic Structure of Atoms: The Bohr Model and Quantum Theory

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