Question 1

Calculate the energy of the red light emitted by a neon atom with a wavelength of 703 nm.

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Question 2

Which of the following transitions (in a hydrogen atom) represent absorption of the smallest frequency photon?

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Question 3

Which of the following transitions (in a hydrogen atom) represent emission of the longest wavelength photon?

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Question 4

Which of the following transitions represent the emission of a photon with the largest energy?

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Question 5

Calculate the frequency of the green light emitted by a hydrogen atom with a wavelength of 486.1 nm.

Accepted Answer

We can use the equation:

c = λν

where c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength (486.1 nm), and ν is the frequency (in Hz).

First, we need to convert the wavelength to meters:

λ = 486.1 nm = 4.861 x 10^-7 m

Now we can plug in the values and solve for ν:

3.00 x 10^8 m/s = (4.861 x 10^-7 m)ν

ν = (3.00 x 10^8 m/s)/(4.861 x 10^-7 m)
ν = 6.172 x 10^14 Hz

Therefore, the frequency of the green light emitted by the hydrogen atom is 6.172 x 10^14 Hz. Choice D is the correct answer.

Question 6

Calculate the wavelength of light absorbed by a hydrogen atom when an electron undergoes an n = 2 to n = 4 transmission.

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Question 7

How much energy (in kJ) do 3.0 moles of photons, all with a wavelength of 655 nm, contain?

Accepted Answer

We can use the formula E = hc/λ, where E is the energy of a single photon, h is Planck's constant, c is the speed of light, and λ is the wavelength.

First, we need to convert the wavelength from nanometers to meters:

655 nm = 655 x 10^-9 m

Now, we can plug in the values and solve for E:

E = (6.626 x 10^-34 J s) x (2.998 x 10^8 m/s) / (655 x 10^-9 m)

E = 3.035 x 10^-19 J

This is the energy of a single photon. To find the total energy of 3.0 moles of photons, we need to multiply by Avogadro's number and by the number of moles:

Total energy = (3.035 x 10^-19 J/photon) x (6.022 x 10^23 photons/mol) x 3.0 mol

Total energy = 5.48 x 10^5 J

Convert to kJ:

Total energy = 548 kJ

Therefore, the best choice is D, which is 548 kJ.

Question 8

Calculate the energy of the green light emitted, per photon, by a mercury lamp with a frequency of 5.49 × 10¹⁴ Hz.

Accepted Answer

The energy of a photon can be calculated using the formula E = hf, where h is Planck's constant (6.626 × 10^-34 J·s) and f is the frequency of the light. Substituting the given frequency (5.49 × 10^14 Hz) into the formula gives E = (6.626 × 10^-34 J·s)(5.49 × 10^14 Hz) = 3.64 × 10^-19 J.

Question 9

How many photons are contained in a burst of yellow light (589 nm) from a sodium lamp that contains 609 kJ of energy?

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Question 10

What total energy (in kJ) is contained in 1.0 mol of photons, all with a frequency of 2.75 × 10¹⁴ Hz?

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Question 11

Determine the longest wavelength of light required to remove an electron from a sample of potassium metal if the binding energy for an electron in potassium metal is 1.76 × 10³ kJ mol^-1.

Accepted Answer

The energy required to remove an electron from a metal is given by the binding energy. We can use the following formula to relate the binding energy to the longest wavelength of light required to remove an electron:

E = hc/λ - BE

where E is the energy of a photon with wavelength λ, h is Planck's constant, c is the speed of light, and BE is the binding energy. Solving for λ, we get:

λ = hc/(E - BE)

Substituting the given values, we get:

λ = (6.626 × 10^-34 J s) × (3.00 × 10^8 m/s) / ((1.76 × 10^3 J/mol) / (6.022 × 10^23 electrons/mol)) - (1.76 × 10^3 J/mol) / (6.022 × 10^23 electrons/mol)

λ = 68.0 nm

Therefore, the longest wavelength of light required to remove an electron from potassium metal is 68.0 nm. The answer is B.

Question 12

Identify the colour of a flame test for sodium.

Accepted Answer

The flame test for sodium produces a yellow color.

Question 13

Calculate the energy of the violet light emitted by a hydrogen atom with a wavelength of 410 nm.

Accepted Answer

The energy of a photon can be calculated using the formula E = hc/λ, where h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (3.00 × 10^8 m/s), and λ is the wavelength in meters. Converting 410 nm to meters (410 × 10^-9 m) and substituting the values gives E ≈ 4.84 × 10^-19 J.

Question 14

How many photons are contained in a flash of green light (525 nm) that contains 189 kJ of energy?

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Question 15

Calculate the wavelength of light emitted from a hydrogen atom when an electron undergoes an n = 8 to n = 4 transmission.

Accepted Answer

The wavelength of light emitted can be calculated using the Rydberg formula for hydrogen: 1/λ = R_H (1/n1² - 1/n2²). For n1 = 4 and n2 = 8, λ ≈ 1940 nm.

Question 16

Identify the colour of a flame test for potassium.

Accepted Answer

The flame test for potassium produces a violet flame.

Question 17

It is possible to determine the ionization energy for hydrogen using the Bohr equation. Calculate the ionization energy for an atom of hydrogen, making the assumption that ionization is the transition from n = 1 to n = ∞.

Accepted Answer

The ionization energy for hydrogen can be calculated using the formula:

E = -RH/n^2

where E is the energy required to remove the electron, RH is the Rydberg constant (2.18 × 10^-18 J), and n is the initial energy level (in this case, n = 1). To ionize hydrogen, we need to remove the electron completely, which means removing it to an infinite distance from the nucleus (n = ∞).

So, the ionization energy is:

E = -RH/n^2 = -2.18 × 10^-18 J / 1^2 - (-2.18 × 10^-18 J / ∞^2) = +2.18 × 10^-18 J

Therefore, the best choice is B, which corresponds to +2.18 × 10^-18 J.

Question 18

Determine the shortest frequency of light required to remove an electron from a sample of Ti metal if the binding energy of titanium is 3.14 × 10³ kJ mol^-1.

Accepted Answer

The energy required to remove an electron is given by E = hν, where h is Planck's constant (6.626 × 10^-34 J·s). First, convert the binding energy from kJ/mol to J/atom: (3.14 × 10^3 kJ/mol) × (10^3 J/kJ) / (6.022 × 10^23 mol^-1) = 5.21 × 10^-19 J. Then, solve for frequency: ν = E/h = (5.21 × 10^-19 J) / (6.626 × 10^-34 J·s) = 7.87 × 10^15 Hz.

Question 19

Choose the transition (in a hydrogen atom) below which represents the absorption of the shortest wavelength photon.

Accepted Answer

The shortest wavelength corresponds to the highest energy transition. The energy difference between n = 1 and n = 2 is the largest among the given options, resulting in the absorption of the shortest wavelength photon.

Question 20

Calculate the energy of the orange light emitted, per photon, by a neon sign with a frequency of 4.89 × 10¹⁴ Hz.

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Quiz 7: The Quantum-Mechanical Model of the Atom