Question 1

What is the energy of a photon that has the same wavelength as a 100-eV electron?

Accepted Answer

The answer of What is the energy of a photon...

Question 2

The energy of the ground state in the Bohr model is -13.6 eV. The energy of the n = 2 is

Accepted Answer

In the Bohr model, the energy levels are given by E_n = -13.6 eV / n^2. For n = 2, E_2 = -13.6 eV / 2^2 = -3.4 eV.

Question 3

What is the wavelength of a neutron having a kinetic energy of 0.025 eV? (The mass of a neutron is 1.67 × 10^-27 kg.)

Accepted Answer

The de Broglie wavelength λ of a particle is given by λ = h/p, where h is Planck's constant (6.626 × 10^-34 Js) and p is the momentum. The momentum p can be found using p = √(2mE), where m is the mass and E is the kinetic energy. Substituting the given values, the wavelength is approximately 1.8 × 10^-10 m.

Question 4

An electron has a kinetic energy of 10 eV. What is the wavelength of this electron?

Accepted Answer

The de Broglie wavelength of an electron is given by λ = h/p, where h is Planck's constant and p is the momentum. For an electron with kinetic energy (KE), p = √(2m_e * KE). Substituting the values, the wavelength is approximately 3.9 × 10^-10 m.

Question 5

The radius of the n = 3 Bohr orbit in the hydrogen atom is

Accepted Answer

The answer of The radius of the n = 3...

Question 6

What is the de Broglie wavelength of an electron whose kinetic energy is 1.0 eV?

Accepted Answer

The de Broglie wavelength λ is given by λ = h/p, where h is Planck's constant and p is the momentum. For an electron with kinetic energy (KE) of 1.0 eV, the momentum p can be calculated using p = sqrt(2mKE), where m is the electron mass. Substituting the values, the de Broglie wavelength is approximately 1.2 nm.

Question 7

What is the magnitude of the energy difference between the lowest energy of a hydrogen atom (n = 1) and the second excited state (n = 3)?

Accepted Answer

The energy levels of a hydrogen atom are given by the formula E_n = -13.6 eV/n^2. For n=1, E_1 = -13.6 eV, and for n=3, E_3 = -13.6 eV/9 = -1.51 eV. The energy difference is |E_1 - E_3| = |-13.6 eV + 1.51 eV| = 12.1 eV.

Question 8

In an electron two-slit experiment, the slits are 15 μm apart. If the first diffraction maximum lies at an angle of 5.0 × 10^-7 rad, what is the momentum of the incoming electrons?

Accepted Answer

The answer of In an electron two-slit experiment, the slits...

Question 9

The energy of the ground state in the Bohr model 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 10

What wavelength corresponds to the n = 2 → n = 1 transition in singly-ionized helium?

Accepted Answer

The answer of What wavelength corresponds to the n =...

Question 11

A beam of X-rays at a certain wavelength are scattered from a free electron at rest and the scattered beam is observed at 45.0° to the incident beam. What is the Compton shift?

Accepted Answer

The answer of A beam of X-rays at a certain...

Question 12

A particle is moving in a circular orbit about a fixed center of a two-dimensional harmonic oscillator. The ground-state (n = 1) energy is 1.0 eV. What is the energy of the second excited level (n = 3)?

Accepted Answer

In a two-dimensional harmonic oscillator, the energy levels are given by E_n = (n + 1)ħω, where n is the quantum number. If the ground state (n=1) energy is 1.0 eV, then the energy of the second excited level (n=3) is 3.0 eV.

Question 13

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

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 14

The de Broglie wavelength of an electron is 380 nm. What is the speed of this electron?

Accepted Answer

The de Broglie wavelength of an electron is given by λ = h/mv where λ = 380 nm, h = Planck's constant, m = mass of electron and v = speed of the electron. Solving for v, we get v = h/(mλ). Substituting the values, we get v = (6.626 x 10^-34 Js)/(9.109 x 10^-31 kg x 380 x 10^-9 m) ≈ 1.92 x 10^6 m/s ≈ 1.92 x 10^1 km/s. Therefore, the correct choice is C.

Question 15

If the momentum of an electron is 1.95 × 10^-27 kg∙m/s, what is its de Broglie wavelength?

Accepted Answer

The de Broglie wavelength (λ) is given by the formula:
λ = h/p
Where h is the Planck's constant and p is the momentum of the particle.

Substituting the given values, we get:
λ = (6.626 × 10^-34 J∙s)/(1.95 × 10^-27 kg∙m/s) 
λ = 3.40 × 10^-7 m 
λ = 340 nm

Therefore, the correct answer is A) 340 nm.

Quiz 37: Early Quantum Theory and Models of the Atom

What is the energy of a photon that has the same wavelength as a 100-eV electron?

The energy of the ground state in the Bohr model is -13.6 eV. The energy of the n = 2 is

What is the wavelength of a neutron having a kinetic energy of 0.025 eV? (The mass of a neutron is 1.67 × 10^-27 kg.)

An electron has a kinetic energy of 10 eV. What is the wavelength of this electron?

The radius of the n = 3 Bohr orbit in the hydrogen atom is

What is the de Broglie wavelength of an electron whose kinetic energy is 1.0 eV?

What is the magnitude of the energy difference between the lowest energy of a hydrogen atom (n = 1) and the second excited state (n = 3) ?

In an electron two-slit experiment, the slits are 15 μm apart. If the first diffraction maximum lies at an angle of 5.0 × 10^-7 rad, what is the momentum of the incoming electrons?

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

What wavelength corresponds to the n = 2 → n = 1 transition in singly-ionized helium?

A beam of X-rays at a certain wavelength are scattered from a free electron at rest and the scattered beam is observed at 45.0° to the incident beam. What is the Compton shift?

A particle is moving in a circular orbit about a fixed center of a two-dimensional harmonic oscillator. The ground-state (n = 1) energy is 1.0 eV. What is the energy of the second excited level (n = 3) ?

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

The de Broglie wavelength of an electron is 380 nm. What is the speed of this electron?

If the momentum of an electron is 1.95 × 10^-27 kg∙m/s, what is its de Broglie wavelength?

Quiz 37: Early Quantum Theory and Models of the Atom

What is the energy of a photon that has the same wavelength as a 100-eV electron?

The energy of the ground state in the Bohr model is -13.6 eV. The energy of the n = 2 is

What is the wavelength of a neutron having a kinetic energy of 0.025 eV? (The mass of a neutron is 1.67 × 10-27 kg.)

An electron has a kinetic energy of 10 eV. What is the wavelength of this electron?

The radius of the n = 3 Bohr orbit in the hydrogen atom is

What is the de Broglie wavelength of an electron whose kinetic energy is 1.0 eV?

What is the magnitude of the energy difference between the lowest energy of a hydrogen atom (n = 1) and the second excited state (n = 3) ?

In an electron two-slit experiment, the slits are 15 μm apart. If the first diffraction maximum lies at an angle of 5.0 × 10-7 rad, what is the momentum of the incoming electrons?

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

What wavelength corresponds to the n = 2 → n = 1 transition in singly-ionized helium?

A beam of X-rays at a certain wavelength are scattered from a free electron at rest and the scattered beam is observed at 45.0° to the incident beam. What is the Compton shift?

A particle is moving in a circular orbit about a fixed center of a two-dimensional harmonic oscillator. The ground-state (n = 1) energy is 1.0 eV. What is the energy of the second excited level (n = 3) ?

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

The de Broglie wavelength of an electron is 380 nm. What is the speed of this electron?

If the momentum of an electron is 1.95 × 10-27 kg∙m/s, what is its de Broglie wavelength?

What is the wavelength of a neutron having a kinetic energy of 0.025 eV? (The mass of a neutron is 1.67 × 10^-27 kg.)

In an electron two-slit experiment, the slits are 15 μm apart. If the first diffraction maximum lies at an angle of 5.0 × 10^-7 rad, what is the momentum of the incoming electrons?

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

If the momentum of an electron is 1.95 × 10^-27 kg∙m/s, what is its de Broglie wavelength?