Question 1

The red line in the hydrogen emission spectrum is 656 nm. If the energy of the nth level is -13.6/n ² eV, then calculate the transition between n levels that this emitted photon comes from. A) n = 2 to n = 3 B) n = 4 to n = 3 C) n = 5 to n = 2 D) n = 3 to n = 2 E) n = 2 to n = 4

Accepted Answer

The energy of the photon emitted can be calculated using the formula:

E = hc/λ

where h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. Substituting the values given:

E = (6.626 x 10^-34 J s) x (3 x 10^8 m/s) / (656 x 10^-9 m)
E = 3.02 x 10^-19 J

We can then use the formula given in the question to find the energy difference between the two levels:

ΔE = -13.6/n_final^2 - (-13.6/n_initial^2)

Since the photon is emitted, we know that the final level is lower than the initial level. We can start by assuming the final level is n = 2, which gives:

3.02 x 10^-19 J = -13.6/2^2 - (-13.6/n_initial^2)
n_initial = 3.02 x 10^-19 J / ((13.6/4) - 3.02 x 10^-19 J)
n_initial = 2.97

This is close to n = 3, so we can try that as well:

3.02 x 10^-19 J = -13.6/3^2 - (-13.6/2^2)
n_initial = 3.03

This is even closer to n = 3, so we can conclude that the transition that produced the red line is from n = 3 to n = 2, which corresponds to choice D.

Question 2

What is the magnitude of the change in potential energy for the electron in the hydrogen atom as it moves from the n = 2 to n = 3 orbit? The radius of the first Bohr orbit is 0.0529 nm.)
A) 1.89 eV
B) 4.91 eV
C) 0.945 eV
D) 3.78 eV
E) None of these is correct.

Accepted Answer

The answer of What is the magnitude of the change...

Question 3

The electron in a hydrogen atom has an orbital radius of 0.0500 nm. To avoid being pulled into the nucleus by electrostatic attraction, the electron must have an orbital speed of A) 7.12 km/s. B) 25.2 km/s. C) 1.02 × 10⁶ m/s. D) 2.25 × 10⁶ m/s. E) 5.0 × 10⁸ m/s.

Accepted Answer

The correct orbital speed can be calculated using the formula for centripetal force, which is balanced by the electrostatic force. For a hydrogen atom, this speed is approximately 2.25 × 10^6 m/s.

Question 4

Light of wavelength 411 nm is observed from a hydrogen discharge tube. What transition produces this emission? The energy of the n = 1 level is -13.6 eV.
A) n = 1.13 to n =1
B) n = 6 to n = 2
C) n = 3 to n = 3
D) n = 2 to n = 6
E) n = 5 to n = 1

Accepted Answer

The wavelength of 411 nm corresponds to a transition between the energy levels of n=6 and n=2. We can use the formula for the energy of a hydrogen atom in a particular energy level to confirm this:

E = -13.6 eV/n^2

For n=2, the energy is:

E = -13.6 eV/2^2 = -3.4 eV

For n=6, the energy is:

E = -13.6 eV/6^2 = -0.75 eV

The difference in energy between these levels is:

ΔE = (-0.75 eV) - (-3.4 eV) = 2.65 eV

We can use the formula for the energy of a photon to calculate the wavelength:

E = hc/λ

where h is Planck's constant, c is the speed of light, and λ is the wavelength. Solving for λ:

λ = hc/E = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s)/(2.65 eV)(1.60 x 10^-19 J/eV) = 410 nm

This is a very close match to the observed wavelength of 411 nm, which confirms that the transition between n=6 and n=2 is responsible for the emission.

Question 5

According to Bohr's model, the radius of an electron orbit for n = 4 in a hydrogen atom is
A) 0.212 nm.
B) 0.846 nm.
C) 0.0265 nm.
D) 0.00331 nm.
E) None of these is correct.

Accepted Answer

The formula for calculating the radius of an electron's orbit in Bohr's model is r = (0.529 * n^2) / Z, where n is the principal quantum number and Z is the atomic number. For hydrogen (Z = 1) with n = 4, the radius would be r = (0.529 * 4^2) / 1 = 8.48 x 10^-10 m, which is equivalent to 0.846 nm. Therefore, the correct answer is B.

Question 6

The energy of the nth level in a one-electron atom is . Consider a beryllium ion with all but one of its electrons removed a beryllium atom normally has four electrons). What is the wavelength of a photon emitted when the electron makes the transition from the third-lowest to the lowest energy state? A) 1.03 × 10^-7 m B) 2.03 × 10^-8 m C) 6.43 × 10^-9 m D) 5.71 × 10^-9 m E) 1.03 × 10^-27 m

Accepted Answer

The answer of The energy of the nth level in...

Question 7

6 eV. The binding energy of the second n = 2) level of the hydrogen atom is
A) +13.6 eV.
B) -13.6 eV.
C) -3.4 eV.
D) -54.8 eV.
E) +3.4 eV.

Accepted Answer

The binding energy of an electron in the hydrogen atom is given by the formula E_n = -13.6 eV / n^2. For n = 2, E_2 = -13.6 eV / 2^2 = -3.4 eV.

Question 8

A photon of wavelength 80 nm is absorbed by the electron in the ground-state level of the hydrogen atom. Is this enough energy to ionize the atom? If so calculate the kinetic energy of the free electron.
A) No, ionization does not occur.
B) Yes, 1.9 eV.
C) Yes, 12 eV.
D) Yes, 29 eV.
E) Yes, 19 eV.

Accepted Answer

The energy required to ionize a hydrogen atom from its ground state is 13.6 eV. The energy of a photon is given by $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{m}^2 \, \text{kg} / \text{s}$), $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\lambda$ is the wavelength of the photon. Substituting the given wavelength of 80 nm ($80 \times 10^{-9} \, \text{m}$), we find the photon's energy to be approximately 15.5 eV. Since this is greater than 13.6 eV, ionization occurs. The kinetic energy of the ejected electron is the difference between the photon's energy and the ionization energy, which is $15.5 \, \text{eV} - 13.6 \, \text{eV} = 1.9 \, \text{eV}$.

Question 9

According to the Bohr theory, the allowed energy states for the hydrogen atom are given by the relation  .This formula can be readily extended to other hydrogenic one-electron) systems. The energy of the second level n = 2) for the doubly ionized lithium atom is
A) -54.4 eV.
B) 13.6 eV.
C) -30.6 eV.
D) -3.4 eV.
E) -1.5 eV.

Accepted Answer

The energy levels of a one-electron atom are given by:

$E_n = -\frac{Z^2}{n^2}	imes13.6	ext{ eV}$

where $Z$ is the atomic number of the nucleus and $n$ is the principal quantum number (n=1,2,3,...).

For the doubly ionized lithium atom (Li$^{2+}$), $Z=3$, so the energy of the second level can be calculated as follows:

$E_2 = -\frac{(3)^2}{2^2}	imes13.6	ext{ eV} = -30.6	ext{ eV}$

Therefore, the best choice is C.

Question 10

In the Bohr model of the hydrogen atom, what is the ratio of the speed of the electron moving in the n = 2 orbit divided by the speed of the electron in the n = 3 orbit?
A) 0.66
B) 1.5
C) 2.25
D) 0.44
E) Its speed is independent of n.

Accepted Answer

In the Bohr model, the speed of an electron in orbit is inversely proportional to the principal quantum number n. Therefore, the speed ratio for n=2 and n=3 is (3/2) = 1.5.

Question 11

An electron in a hydrogen atom jumps from the n = 5 to n = 3 level. Is a photon absorbed or emitted in this process? What is the wavelength of the photon? State whether the photon is in the visible, ultraviolet, or infrared range of the electromagnetic spectrum.
A) absorbed, 1280 nm, infrared
B) emitted, 605 nm, visible
C) emitted, 1280 nm, infrared
D) absorbed, 605 nm, visible
E) emitted, 605 nm, infrared

Accepted Answer

The answer of An electron in a hydrogen atom jumps...

Question 12

The energy associated with the lowest n = 1 state in a hydrogen atom is - 13.6 eV. The wavelength of the emission line corresponding to the transition from n = 4 to n = 3 is A) 1.9 × 10^-6 m. B) 8.2 × 10^-7 m. C) 5.3 × 10⁵ m. D) 3.0 × 10^-25 m. E) 1.6 × 10¹⁴ m.

Accepted Answer

The answer of The energy associated with the lowest n...

Question 13

What is the ratio of the radius of the n = 3 orbit to that of the n = 2 orbit?
A) 1.50
B) 4.50
C) 2.25
D) 0.666
E) None of these is correct.

Accepted Answer

The formula for the radius of an electron's orbit in hydrogen atom is given by $r_n=\frac{n^2h^2\epsilon_0}{\pi m e^2}$, where $n$ is the principal quantum number, $h$ is the Planck's constant, $\epsilon_0$ is the permittivity of free space, $m$ is the mass of electron, and $e$ is the elementary charge.

Therefore, the ratio of the radius of the n=3 orbit to that of the n=2 orbit is

$$\frac{r_3}{r_2}=\frac{(3^2)}{(2^2)}=\frac{9}{4}=2.25$$

Therefore, the correct answer is (C).

Question 14

Using Bohr's model, the speed of an electron in the first orbit is A) 3.14 × 10⁵m/s. B) 1.09 × 10⁶ m/s. C) 1.37 × 10⁷ m/s. D) 2.19 × 10⁶ m/s. E) None of these is correct.

Accepted Answer

According to Bohr's model, the speed of an electron in the first orbit is given by v = (Z * e^2) / (4 * pi * epsilon0 * h), where Z is the atomic number, e is the electron charge, epsilon0 is the permittivity of free space, and h is Planck's constant. For hydrogen, Z = 1. Plugging in the values and solving for v gives v = 2.19 × 10^6 m/s. Therefore, the correct answer is D.

Question 15

The radius of the n = 1 Bohr orbit in the hydrogen atom is 0.053 nm. What is the radius of the n = 5 Bohr orbit?
A) 50.053) nm
B) 250.053) nm
C) 0.053 nm
D) 1/5)0.053) nm
E) 1/25)0.053) nm

Accepted Answer

The radius of the nth Bohr orbit is given by the formula: 
rn = (n^2)*r1
Where r1 is the radius of the first Bohr orbit (n=1).
So for n=5, 
r5 = (5^2)*0.053 nm
r5 = 13.25 nm
Hence, the answer is option B.

Question 16

The radii of the Bohr orbits in atomic hydrogen are given by  .If the radius of the first Bohr orbit n = 1) is 0.053 nm, the radius of the third Bohr orbit n = 3) is
A) 0.16 nm.
B) 0.018 nm.
C) 0.48 nm.
D) 0.35 nm.
E) 1.3 nm.

Accepted Answer

The radius of the nth Bohr orbit is given by $r_n=n^2\cdot r_1$, where $r_1$ is the radius of the first Bohr orbit. Thus, $r_3=3^2\cdot 0.053\; \mathrm{nm}=0.48\; \mathrm{nm}$. Therefore, the correct choice is (C).

Question 17

Bohr's quantum condition on electron orbits required A) that the angular momentum of the electron about the hydrogen nucleus equal nh/2π). B) that no more than one electron occupy a given stationary state. C) the electrons to spiral into the nucleus while radiating electromagnetic waves. D) that the energies of an electron in a hydrogen atom be equal to nE_o, where E_o is a constant energy and n is an integer. E) None of these is correct.

Accepted Answer

Bohr's quantum condition states that the angular momentum of the electron orbiting the hydrogen nucleus must be quantized and equal to nh/2π, where n is a positive integer. This is known as the quantization of angular momentum. Option B is also true for the Pauli exclusion principle, but it is not relevant to Bohr's quantum condition. Option C is false because Bohr's quantum condition allowed for stable electron orbits, while spiral movements would lead to instability. Option D is incorrect because it includes terms not part of Bohr's quantum condition.

Question 18

The radius of the n = 1 orbit in the hydrogen atom is 0.053 nm. What is the radius of the n = 3 orbit of a singly charged lithium, which has three protons in its nucleus?
A) 30.053) nm
B) 90.053) nm
C) 0.053 nm
D) 1/3)0.053) nm
E) 1/9)0.053) nm

Accepted Answer

The radius of the orbit is proportional to n^2 and inversely proportional to the atomic number. Lithium has three protons, so the radius of the n = 3 orbit is 3^2/1^2 * 0.053 nm = 0.477 nm.

Question 19

The equation derived by Bohr for the wavelengths of λ of the lines in hydrogen- like spectra is .The first member of the Balmer series of hydrogen has λ = 660 nm. Doubly ionized is hydrogen-like. The wavelength of the first member of the Balmer series for doubly ionized is A) 73 nm. B) 5.9 × 10³ nm. C) 150 nm. D) 60 nm. E) 1.8 × 10^-3 nm.

Accepted Answer

The answer of The equation derived by Bohr for the...

Question 20

The energy of the nth level in a one-electron atom is  . Consider a beryllium ion with all but one of its electrons removed a beryllium atom normally has four electrons). What is the energy of the electron when it is in the third-lowest energy state?
A) -24 eV
B) -7.6 eV
C) -1.5 eV
D) 24 eV
E) 7.6 eV

Accepted Answer

The answer of The energy of the nth level in...

Quiz 26: Quantum Physics and Atomic Structure

The red line in the hydrogen emission spectrum is 656 nm. If the energy of the nth level is -13.6/n ² eV, then calculate the transition between n levels that this emitted photon comes from.

What is the magnitude of the change in potential energy for the electron in the hydrogen atom as it moves from the n = 2 to n = 3 orbit? The radius of the first Bohr orbit is 0.0529 nm.)

The electron in a hydrogen atom has an orbital radius of 0.0500 nm. To avoid being pulled into the nucleus by electrostatic attraction, the electron must have an orbital speed of

Light of wavelength 411 nm is observed from a hydrogen discharge tube. What transition produces this emission? The energy of the n = 1 level is -13.6 eV.

According to Bohr's model, the radius of an electron orbit for n = 4 in a hydrogen atom is

6 eV. The binding energy of the second n = 2) level of the hydrogen atom is

A photon of wavelength 80 nm is absorbed by the electron in the ground-state level of the hydrogen atom. Is this enough energy to ionize the atom? If so calculate the kinetic energy of the free electron.

According to the Bohr theory, the allowed energy states for the hydrogen atom are given by the relation .This formula can be readily extended to other hydrogenic one-electron) systems. The energy of the second level n = 2) for the doubly ionized lithium atom is

In the Bohr model of the hydrogen atom, what is the ratio of the speed of the electron moving in the n = 2 orbit divided by the speed of the electron in the n = 3 orbit?

An electron in a hydrogen atom jumps from the n = 5 to n = 3 level. Is a photon absorbed or emitted in this process? What is the wavelength of the photon? State whether the photon is in the visible, ultraviolet, or infrared range of the electromagnetic spectrum.

The energy associated with the lowest n = 1 state in a hydrogen atom is - 13.6 eV. The wavelength of the emission line corresponding to the transition from n = 4 to n = 3 is

What is the ratio of the radius of the n = 3 orbit to that of the n = 2 orbit?

Using Bohr's model, the speed of an electron in the first orbit is

The radius of the n = 1 Bohr orbit in the hydrogen atom is 0.053 nm. What is the radius of the n = 5 Bohr orbit?

The radii of the Bohr orbits in atomic hydrogen are given by .If the radius of the first Bohr orbit n = 1) is 0.053 nm, the radius of the third Bohr orbit n = 3) is

Bohr's quantum condition on electron orbits required

The radius of the n = 1 orbit in the hydrogen atom is 0.053 nm. What is the radius of the n = 3 orbit of a singly charged lithium, which has three protons in its nucleus?

The equation derived by Bohr for the wavelengths of λ of the lines in hydrogen- like spectra is .The first member of the Balmer series of hydrogen has λ = 660 nm. Doubly ionized is hydrogen-like. The wavelength of the first member of the Balmer series for doubly ionized is

The energy of the nth level in a one-electron atom is . Consider a beryllium ion with all but one of its electrons removed a beryllium atom normally has four electrons) . What is the energy of the electron when it is in the third-lowest energy state?