Question 1

A hydrogen atom initially in the n = 6 state decays to the n = 2 state. The emitted photon is detected in a photographic plate. What is the wavelength of the detected photon? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s) A) 410 nm B) 93.8 nm C) 1090 nm D) 93.1 nm

Accepted Answer

The energy difference between the initial and final states is calculated using the formula for the energy levels of a hydrogen atom: $E_n = \frac{-13.6 \text{ eV}}{n^2}$. The energy of the photon emitted is $E = E_{initial} - E_{final} = \frac{-13.6 \text{ eV}}{6^2} - \frac{-13.6 \text{ eV}}{2^2}$. Converting this energy difference to joules and using $E = \frac{hc}{\lambda}$ allows solving for $\lambda$, the wavelength of the photon, which is approximately 410 nm.

Question 2

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12 m. (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 10^-19 J)

Accepted Answer

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Question 3

Light shines through atomic hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.63 nm. What is the value of n of the level to which the hydrogen is being excited by the absorption of light of this wavelength? Assume that the most of the atoms in the gas are in the lowest level. (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J, the Rydberg constant is R = 1.097 × 10⁷ m^-1) A) 14 B) 16 C) 11 D) 21

Accepted Answer

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Question 4

What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R = 1.097 × 10⁷ m^-1,^c= 3.00 × 10⁸ m/s) A) 2.86 × 10¹³ Hz B) 1.43 × 10¹³ Hz C) 7.46 × 10¹³ Hz D) 8.82 × 10¹³ Hz E) 1.05 × 10¹³ Hz

Accepted Answer

The frequency of the light emitted by atomic hydrogen can be calculated using the formula derived from the Rydberg formula for hydrogen emission: $$f = R \cdot c \cdot \left( \frac{1}{m^2} - \frac{1}{n^2} \right)$$ where $R$ is the Rydberg constant ($1.097 \times 10^{7} \, \text{m}^{-1}$), $c$ is the speed of light ($3.00 \times 10^{8} \, \text{m/s}$), $m$ is the lower energy level (8), and $n$ is the higher energy level (12). Plugging in the values: $$f = 1.097 \times 10^{7} \times 3.00 \times 10^{8} \times \left( \frac{1}{8^2} - \frac{1}{12^2} \right) = 2.86 \times 10^{13} \, \text{Hz}$$.

Question 5

Light of wavelength 105 nm falls on a metal surface for which the work function is 5.00 eV. What is the minimum de Broglie wavelength of the photoelectrons emitted from this metal? (h = 6.626 × 10^-34 J ∙ s = 4.14 × 10^-15 eV ∙ s, c = 3.00 × 10⁸ m/s, m_e_l = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J) A) 0.24 nm B) 0.33 nm C) 0.47 nm D) 0.66 nm E) 0.94 nm

Accepted Answer

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Question 6

Electrons emerge from an electron gun with a speed of 2.0 × 10⁶ m/s and then pass through a pair of thin parallel slits. Interference fringes with a spacing of 2.7 mm are detected on a screen far from the double slit and fairly close to the center of the pattern. What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? (m_el = 9.11 × 10^-31 kg, m_neutron = 1.67 × 10^-27 kg) A) 1.5 µm B) 4.9 µm C) 0.93 nm D) 1.1 µm E) 1.5 nm

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Question 7

The energy of the ground state in the Bohr model of the hydrogen atom is -13.6 eV. In a transition from the n = 2 state to the n = 4 state, a photon of energy
A) 3.40 eV is emitted.
B) 3.40 eV is absorbed.
C) 2.55 eV is emitted.
D) 2.55 eV is absorbed.
E) 0.85 eV is absorbed.

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Question 8

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy 8.5 eV. What is the energy of the resulting free electron? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J) A) 5.1 eV B) 6.6 eV C) 6.9 eV D) 7.6 eV

Accepted Answer

First, we need to find the final energy state of the hydrogen atom after the electron absorbs the photon. We can use the formula:

ΔE = hf = (E2 - E1)

where ΔE is the change in energy, h is Planck's constant, f is the frequency of the photon, and E2 and E1 are the energy levels before and after the absorption, respectively.

We know that the atom is in its n=2 excited state before the absorption, which corresponds to an energy level of:

E2 = -13.6 eV / 2² = -3.4 eV

We also know the energy of the absorbed photon, which is given as 8.5 eV. Therefore:

ΔE = hf = 8.5 eV

So, we can solve for the final energy level of the electron:

E1 = E2 + ΔE = -3.4 eV + 8.5 eV = 5.1 eV

Finally, we need to find the energy of the resulting free electron. Since the electron is now free (i.e. not bound to the hydrogen nucleus), its energy is simply the same as the final energy level we just calculated:

5.1 eV

Therefore, the answer is A) 5.1 eV.

Question 9

Light excites atomic hydrogen from its lowest level to the n = 4 level. What is the energy of the light? The energy of the lowest level is -13.6 eV.
A) 12.8 eV
B) 3.40 eV
C) 0.850 eV
D) 26.4 eV

Accepted Answer

The energy of an electron in a hydrogen atom is given by $E_n = \frac{-13.6 \text{ eV}}{n^2}$, where $n$ is the principal quantum number. For the lowest level (n=1), $E_1 = -13.6 \text{ eV}$, and for the n=4 level, $E_4 = \frac{-13.6 \text{ eV}}{4^2} = \frac{-13.6 \text{ eV}}{16} = -0.85 \text{ eV}$. The energy of the light that excites the atom from n=1 to n=4 is the difference in energy levels: $E = E_4 - E_1 = -0.85 \text{ eV} - (-13.6 \text{ eV}) = 12.75 \text{ eV}$, which is approximately 12.8 eV.

Question 10

Suppose that in a parallel universe, the proton and electron were identical to their counterparts in our own universe EXCEPT that the electron had twice as much charge as our electron. In our present universe, the radius of the first Bohr orbit for hydrogen is a₀ and the speed of an electron in that orbit is v₀. In the parallel universe (a) what would be the radius (in terms of a₀) of the first Bohr orbit for hydrogen? (b) what would be the speed (in terms of v₀) of an electron in the first Bohr orbit for hydrogen?

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Question 11

A nonrelativistic electron has a kinetic energy of 5.4 eV. What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J) A) 2.4 keV B) 2.2 keV C) 2.0 keV D) 2.5 keV E) 2.7 keV

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Question 12

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 10⁴ m/s? (m_proton = 1.67 × 10^-27 kg, c = 3.00 × 10⁸ m/s) A) 220 keV B) 150 keV C) 290 keV D) 360 keV E) 440 keV

Accepted Answer

The de Broglie wavelength λ of a proton is given by λ = h / (m * v), where h is Planck's constant (6.626 × 10^-34 Js), m is the mass of the proton, and v is its velocity. Calculate λ and then use E = hc / λ to find the energy of the photon. The energy is approximately 220 keV.

Question 13

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J) A) 2000 m/s B) 1900 m/s C) 1700 m/s D) 1600 m/s E) 1400 m/s

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Question 14

In a double slit experiment, a beam of electrons strikes a pair of slits. The slits are 15 μm apart, and the first interference maximum lies at an angle of 0.50 µrad from the center of the interference pattern. What is the momentum of the incoming electrons? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg) A) 4.4 × 10^-23 kg ∙ m/s B) 2.2 × 10^-23 kg ∙ m/s C) 1.1 × 10^-23 kg ∙ m/s D) 6.6 × 10^-23 kg ∙ m/s E) 8.8 × 10^-23 kg ∙ m/s

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Question 15

A hydrogen atom is excited to the n = 10 stated. It then decays to the n = 4 state by emitting a photon which is detected in a photographic plate. What is the frequency of the detected photon? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J) A) 3.46 × 10¹⁴ Hz B) 0.865 × 10¹⁴ Hz C) 1.27 × 10¹⁴ Hz D) 4.05 × 10¹⁴ Hz E) 1.73 × 10¹⁴ Hz

Accepted Answer

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Question 16

A gas of helium atoms (each of mass 6.65 × 10^-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J ∙ s, the Boltzmann constant is 1.38 × 10^-23 J/K) A) 5.22 × 10^-11 m B) 7.38 × 10^-11 m C) 1.04 × 10^-10 m D) 2.82 × 10^-10 m E) 3.99 × 10^-10 m

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Question 17

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10^-10 m. A) 0.476 nm B) 0.159 nm C) 0.381 nm D) 0.548 nm

Accepted Answer

The orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom is given by:$$r_n = n^2 * a_0$$where n is the principal quantum number and a0 is the Bohr radius.For n = 3, we have:$$r_3 = 3^2 * a_0 = 9 * 0.529 × 10^{−10} m = 4.76 × 10^{−10} m = 0.476 nm$$

Question 18

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s) A) 2.43 μm B) 1.46 μm C) 1.94 μm D) 2.92 μm

Accepted Answer

The energy of a photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. The energy of a hydrogen atom in the n = 20 state is -13.6 eV / (20)^2 = -0.034 eV. The energy of a hydrogen atom in the n = 5 state is -13.6 eV / (5)^2 = -0.544 eV. The energy of the emitted photon is therefore 0.544 eV - 0.034 eV = 0.510 eV. The wavelength of the emitted photon is therefore λ = hc/E = (6.626 × 10^-34 J s)(3.00 × 10^8 m/s) / (0.510 eV * 1.60 × 10^-19 J/eV) = 2.43 μm.

Question 19

A nonrelativistic electron is accelerated from rest through a potential difference. After acceleration the electron has a de Broglie wavelength of 880 nm. What is the potential difference though which this electron was accelerated? (h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-¹⁹ C, m_el = 9.11 × 10^-31 kg) A) 1.9 µV B) 1.7 µV C) 2.2 µV D) 2.5 µV

Accepted Answer

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Question 20

A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of The entire central band of the diffraction pattern is observed at ±90°. The illumination is now replaced by a nonrelativistic beam of electrons, each having a kinetic energy of 980 eV. When this beam hits the slit at normal incidence, at what angle will the first minimum of the electron diffraction pattern occur? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J) A) 0.095 mrad B) 0.071 mrad C) 0.046 mrad D) 0.12 mrad E) 0.14 mrad

Accepted Answer

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Quiz 38: Quantization

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10-12 m. (h = 6.626 × 10-34 J ∙ s, mneutron = 1.675 × 10-27 kg, 1 eV = 1.60 10-19 J)

What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R = 1.097 × 107 m-1, c = 3.00 × 108 m/s)

The energy of the ground state in the Bohr model of the hydrogen atom is -13.6 eV. In a transition from the n = 2 state to the n = 4 state, a photon of energy

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy 8.5 eV. What is the energy of the resulting free electron? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)

Light excites atomic hydrogen from its lowest level to the n = 4 level. What is the energy of the light? The energy of the lowest level is -13.6 eV.

A nonrelativistic electron has a kinetic energy of 5.4 eV. What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (mel = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J)

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 104 m/s? (mproton = 1.67 × 10-27 kg, c = 3.00 × 108 m/s)

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (mel = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J)

A gas of helium atoms (each of mass 6.65 × 10-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10-34 J ∙ s, the Boltzmann constant is 1.38 × 10-23 J/K)

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10-10 m.

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s)

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12 m. (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 10^-19 J)

What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R = 1.097 × 10⁷ m^-1,^c= 3.00 × 10⁸ m/s)

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy 8.5 eV. What is the energy of the resulting free electron? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A nonrelativistic electron has a kinetic energy of 5.4 eV. What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 10⁴ m/s? (m_proton = 1.67 × 10^-27 kg, c = 3.00 × 10⁸ m/s)

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A gas of helium atoms (each of mass 6.65 × 10^-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J ∙ s, the Boltzmann constant is 1.38 × 10^-23 J/K)

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10^-10 m.

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)