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

$$\lambda = 3.64 \times 10$$^{-10}$$\ \mathrm{m}$$

Question 1

According to the Bohr model, what is the principal reason that electrons in a hydrogen atom do not spiral into the nucleus?

Accepted Answer

Electrons exist only in specific, quantized energy levels and cannot exist between them.

Question 2

Which equation correctly gives 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 $$n=5 to$$ $$n=3. $$What is the wavelength (in nm) of the photon emitted? Use $$R_H = 2.18 	imes 10$$^{-18}$$\ \mathrm{J}$$, $$h = 6.63 	imes 10$$^{-34}$$\ \mathrm{J \cdot s}$$, and $$c = 3.00 	imes 10^8$\ \mathrm{m/s}.$$

Accepted Answer

$$\lambda = 1280\ \mathrm{nm}$$

Question 4

Which of the following best describes the limitation of the Bohr model?

Accepted Answer

It only accurately predicts the spectra of hydrogen and fails for multi-electron atoms.

Question 5

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

Accepted Answer

$$\lambda = 3.64 	imes 10$$^{-10}$$\ \mathrm{m}$$

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 statement about the Heisenberg uncertainty principle is correct?

Accepted Answer

It is impossible to know both the exact position and exact momentum of a particle simultaneously.

Question 9

Which of the following sets of quantum numbers is NOT allowed for an electron in an atom?

Accepted Answer

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

Question 10

Which orbital is spherical in shape?

Accepted Answer

$$1s$$

Question 11

How many $$p$$ orbitals are there in the $$n=2$$ shell?

Accepted Answer

3

Question 12

Which transition in a hydrogen atom would emit a photon with the highest energy?

Accepted Answer

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

Question 13

What is the value of the principal quantum number $$n$$ for the first shell that contains $$d$$ orbitals?

Accepted Answer

$$n=3$$

Question 14

Which of the following best explains why the wave properties of matter are not observable for macroscopic objects?

Accepted Answer

Planck's constant is extremely small, making the wavelength negligible for large masses.

Question 15

If an electron in a hydrogen atom absorbs a photon and moves from $$n=1 to$$ $$n=3$$, what happens to the energy of the atom?

Accepted Answer

The atom's energy increases by the energy of the absorbed photon.

Question 16

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

Accepted Answer

Magnetic quantum number $$m_l$$

Question 17

How many total orbitals are present in the $$n=3$$ shell?

Accepted Answer

9

Question 18

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

Accepted Answer

$$p$$ orbitals have two lobes with a node at the nucleus.

Question 19

Which of the following is a correct set of quantum numbers for a $$4f$$ orbital?

Accepted Answer

$$n=4,\ l=3,\ m_l=2$$

Question 20

Which quantum number is primarily responsible for determining the size of an orbital?

Accepted Answer

Principal quantum number $$n$$

Electronic Structure of Atoms: The Bohr Model and Quantum Theory

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