Question 1

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,

Accepted Answer

E

Question 2

If the accuracy in measuring the velocity of a particle increases,the accuracy in measuring its position will

Accepted Answer

According to the Heisenberg Uncertainty Principle, increasing the accuracy in measuring the velocity of a particle will decrease the accuracy in measuring its position, as these two quantities are inversely related in terms of their uncertainties.

Question 3

At absolute temperature T,a black body radiates its peak intensity at wavelength λ.At absolute temperature 2T,what would be the wavelength of the peak intensity?

Accepted Answer

Wien's displacement law states that the wavelength of the peak intensity is inversely proportional to the temperature. Therefore, if the temperature doubles, the wavelength of the peak intensity halves.

Question 4

A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength.Which of the following statements about these particles are accurate? (There may be more than one correct choice.)

Accepted Answer

The de Broglie wavelength formula is λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum. If two particles have the same de Broglie wavelength, they must have the same momentum, making choice C correct. For nonrelativistic particles, kinetic energy (KE) is given by KE = p^2/2m, where p is momentum and m is mass. Since the electron has a much smaller mass than the proton, for the same momentum, the electron will have more kinetic energy, making choice D correct.

Question 5

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy .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)

Accepted Answer

The answer of A hydrogen atom is in its n...

Question 6

The Bohr radius of the hydrogen atom is 0.529 × 10^-10 m.What is the radius of the n = 2 state?

Accepted Answer

The radius of the n-th state in a hydrogen atom is given by n² times the Bohr radius. For n = 2, the radius is 2² × 0.529 × 10⁻¹⁰ m = 2.12 × 10⁻¹⁰ m.

Question 7

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, ,the Rydberg constant is R = 1.097 × 10⁷ m^-1)

Accepted Answer

The answer of Light shines through atomic hydrogen gas.It is...

Question 8

In the vicinity of what frequency does an object with a temperature of 1000 K radiate the largest amount of power? (c = 3.00 × 10⁸ m/s,Wien displacement law constant equals ,σ = 5.670 × 10^-8 W/m² • K⁴)

Accepted Answer

The answer of In the vicinity of what frequency does...

Question 9

If the accuracy in measuring the position of a particle increases,the accuracy in measuring its velocity will

Accepted Answer

This is due to the Heisenberg Uncertainty Principle, which states that increasing the accuracy in measuring the position of a particle necessarily decreases the accuracy in measuring its velocity, and vice versa.

Question 10

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

Accepted Answer

The answer of The energy of the ground state in...

Question 11

A perfectly black body at 100°C emits light of intensity I that has the strongest intensity near wavelength λ.The temperature of this body is now increased to 200°C.
(a)In terms of I,what is the intensity at which this hotter body radiates?
(b)In terms of λ,near what wavelength does light radiated from this hotter body have the strongest intensity?

Accepted Answer

The answer of A perfectly black body at 100°C emits...

Question 12

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.)

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 13

What is the wavelength of peak emission for a black body at 37°C? (c = 3.0 × 10⁸ m/s,Wien displacement law constant is 2.9 × 10^-3 m • K,σ = 5.67 × 10^-8 W/m² • K⁴)

Accepted Answer

We can use Wien's displacement law to determine the wavelength of peak emission:
λ_peak = b/T
where b is the Wien displacement law constant and T is the temperature in Kelvin.
Converting 37°C to Kelvin: 
T = 37°C + 273.15 = 310.15 K
Substituting values: 
λ_peak = (2.9 × 10^-3 m • K) / 310.15 K
λ_peak = 9.39 x 10^-6 m or 9.4 µm
Therefore, the answer is B.

Question 14

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,

Accepted Answer

The answer of A hydrogen atom initially in the n...

Question 15

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

Accepted Answer

The answer of What is the orbital radius of the...

Question 16

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?

Accepted Answer

The answer of Suppose that in a parallel universe,the proton...

Question 17

Which of the following are characteristics of laser light? (There may be more than one correct choice.)

Accepted Answer

Laser light is coherent, meaning that it has a fixed phase relationship between the electric and magnetic fields. It is also produced by an inverted population of atoms, where more atoms are in higher energy levels than in lower levels, resulting in stimulated emission of radiation. Laser light does not contain a full spectrum of wavelengths, as it is composed of only one specific wavelength.

Question 18

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.

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 19

A hydrogen atom makes a downward transition from the 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)

Accepted Answer

The answer of A hydrogen atom makes a downward transition...

Question 20

The energy of the ground state in the Bohr model of the hydrogen atom is -13.6 eV.The energy of the n = 2 state of hydrogen in this model is closest to

Accepted Answer

The energy levels in the Bohr model of the hydrogen atom are given by $E_n = \frac{-13.6 \text{ eV}}{n^2}$, where $n$ is the principal quantum number. For the $n = 2$ state, the energy is $E_2 = \frac{-13.6 \text{ eV}}{2^2} = \frac{-13.6 \text{ eV}}{4} = -3.4 \text{ eV}$.

Quiz 39: Particles Behaving As Waves

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,

If the accuracy in measuring the velocity of a particle increases,the accuracy in measuring its position will

At absolute temperature T,a black body radiates its peak intensity at wavelength λ.At absolute temperature 2T,what would be the wavelength of the peak intensity?

A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength.Which of the following statements about these particles are accurate? (There may be more than one correct choice.)

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy .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)

The Bohr radius of the hydrogen atom is 0.529 × 10-10 m.What is the radius of the n = 2 state?

In the vicinity of what frequency does an object with a temperature of 1000 K radiate the largest amount of power? (c = 3.00 × 108 m/s,Wien displacement law constant equals ,σ = 5.670 × 10-8 W/m2 • K4)