Q: In Millikan’s oil drop experiment, what fundamental constant was determined?

The elementary charge $$e = 1.602 \times 10$$^{-19}$$ \ \mathrm{C}$$

Q: A sodium vapor lamp emits monochromatic light of wavelength $$589 \ \mathrm{nm}$$ and has a power output of $$50 \ \mathrm{W}. $$How many photons does it emit per second? (Use $$h = 6.626 \times 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$c = 3.00 \times 10^8$ \ \mathrm{m/s})$$

$$1.48 \times 10$$^{20}$$ photons/s

Q: Calculate the change in wavelength $$\Delta \lambda$$ for a photon scattered at $$60^\circ by an $$electron at rest. ($$h = 6.626 \times 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$m_e = 9.11 \times 10$$^{-31}$$ \ \mathrm{kg}$$, $$c = 3.00 \times 10^8$ \ \mathrm{m/s})$$

$$1.2 \times 10$$^{-12}$$ \ \mathrm{m}$$

Question 1

Which experiment led to the discovery of the electron and what key property did J.J. Thomson measure?

Accepted Answer

The cathode ray tube experiment; the charge-to-mass ratio $$\left( \frac{q}{m} \right) of $$the electron

Question 2

In Millikan’s oil drop experiment, what fundamental constant was determined?

Accepted Answer

The elementary charge $$e = 1.602 	imes 10$$^{-19}$$ \ \mathrm{C}$$

Question 3

According to Wien’s Law, how does the wavelength of maximum emission $$\lambda_{max} of a $$blackbody change with temperature?

Accepted Answer

$$\lambda_{max} is $$inversely proportional to temperature

Question 4

A sodium vapor lamp emits monochromatic light of wavelength $$589 \ \mathrm{nm}$$ and has a power output of $$50 \ \mathrm{W}. $$How many photons does it emit per second? (Use $$h = 6.626 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$c = 3.00 	imes 10^8$ \ \mathrm{m/s})$$

Accepted Answer

$$1.48 	imes 10$$^{20}$$ photons/s

Question 5

Which observation from the photoelectric effect experiment could NOT be explained by classical wave theory?

Accepted Answer

Electrons are emitted only if the light frequency exceeds a threshold, regardless of intensity

Question 6

A metal surface is illuminated with light of wavelength $$340 \ \mathrm{nm}$$, and electrons are ejected with a maximum kinetic energy of $$1.2 \ \mathrm{eV}. $$What is the work function $$\phi of $$the metal? ($$h = 6.626 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$c = 3.00 	imes 10^8$ \ \mathrm{m/s}$$, $$1 \ \mathrm{eV} = 1.6 	imes 10$$^{-19}$$ \ \mathrm{J})$$

Accepted Answer

$$2.45 \ \mathrm{eV}$$

Question 7

The Compton effect demonstrates that:

Accepted Answer

Photons have momentum and can transfer it to electrons

Question 8

Calculate the change in wavelength $$\Delta \lambda$$ for a photon scattered at $$60^\circ by an $$electron at rest. ($$h = 6.626 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$m_e = 9.11 	imes 10$$^{-31}$$ \ \mathrm{kg}$$, $$c = 3.00 	imes 10^8$ \ \mathrm{m/s})$$

Accepted Answer

$$1.2 	imes 10$$^{-12}$$ \ \mathrm{m}$$

Question 9

According to de Broglie’s hypothesis, what is the wavelength of a particle with momentum $$p$$?

Accepted Answer

$$\lambda = \frac{h}{p}$$

Question 10

Which experimental observation provided evidence for the wave nature of electrons?

Accepted Answer

Electron diffraction by crystals

Question 11

Which statement best describes the Rutherford model of the atom?

Accepted Answer

Electrons orbit a small, dense, positively charged nucleus

Question 12

The Balmer series in the hydrogen spectrum corresponds to electronic transitions ending at which energy level?

Accepted Answer

$$n = 2$$

Question 13

According to Bohr’s model, what is the quantized angular momentum of an electron in the $$nth $$orbit?

Accepted Answer

$$L = n \frac{h}{2\pi}$$

Question 14

Which of the following best explains why electrons in Bohr’s orbits do not radiate energy?

Accepted Answer

Their orbits correspond to standing waves, so no energy is lost

Question 15

A 5.3 MeV $$\alpha-$$particle (mass $$= 6.64 	imes 10$$^{-27}$$ \ \mathrm{kg}) $$has what de Broglie wavelength? ($$1 \ \mathrm{eV} = 1.6 	imes 10$$^{-19}$$ \ \mathrm{J}$$, $$h = 6.626 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s})$$

Accepted Answer

$$6.24 	imes 10$$^{-15}$$ \ \mathrm{m}$$

Question 16

Which of the following is a consequence of the quantization of energy levels in the Bohr model?

Accepted Answer

Atoms emit light only at specific wavelengths

Question 17

What is the energy of the ground state of the hydrogen atom according to the Bohr model?

Accepted Answer

$$-13.6 \ \mathrm{eV}$$

Question 18

Which formula gives the wavelength of the photon emitted when an electron transitions from level $$n_i to$$ $$n_f in $$hydrogen?

Accepted Answer

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

Early Quantum Theory and Models of the Atom: Study Notes

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