Question 1

According to Bohr's model of the hydrogen atom, the radius of the first orbit (Bohr radius) is approximately:

Accepted Answer

The Bohr radius a₀ = 0.53 Å is the characteristic radius of the first electron orbit in a hydrogen atom.

Question 2

The energy of an electron in the second orbit (n=2) of a hydrogen atom is -3.4 eV. What is the energy of the electron in the first orbit (n=1)?

Accepted Answer

Energy in Bohr model: Eₙ = -13.6/n² eV, so E₁ = -13.6/1² = -13.6 eV.

Question 3

An electron transitions from the third orbit (n=3) to the second orbit (n=2) in a hydrogen atom. The energy of the emitted photon is:

Accepted Answer

ΔE = 13.6(1/2² - 1/3²) = 13.6(1/4 - 1/9) = 13.6 × 5/36 ≈ 1.9 eV.

Question 4

Which of the following statements about the ground state of a hydrogen atom is correct?

Accepted Answer

In the ground state of hydrogen, the electron is in the n=1 orbit, which is the lowest possible energy state according to Bohr's model.

Question 5

The ionization energy of a hydrogen atom is the energy required to remove the electron from the first orbit. This value is:

Accepted Answer

Ionization energy equals the magnitude of ground state energy: |E₁| = 13.6 eV.

Question 6

Calculate the ionization energy of hydrogen (energy to remove electron from n=1 to n=∞).

Accepted Answer

Ionization energy = E₁ - E∞ = -13.6 - 0 = 13.6 eV (magnitude).

Question 7

Which spectral series corresponds to electron transitions ending at n=2 in a hydrogen atom?

Accepted Answer

The Balmer series results from transitions to n=2 (visible light range for hydrogen).

Question 8

An atom has electrons in orbitals with quantum numbers. What is the minimum number of electrons needed to fill the K and L shells completely?

Accepted Answer

K shell (n=1) holds 2e⁻ and L shell (n=2) holds 8e⁻; total = 2 + 8 = 10 electrons.

Question 9

In the Bohr model, the velocity of an electron in the nth orbit of hydrogen is proportional to which of the following?

Accepted Answer

From Bohr's model, v_n = (e²/2ε₀h) × (1/n), so velocity is inversely proportional to n.

Question 10

An electron in a hydrogen atom transitions from n=3 to n=1. What is the energy released in this transition? (Use E_n = -13.6/n² eV)

Accepted Answer

Energy released = E₁ - E₃ = -13.6 - (-13.6/9) = -13.6 + 1.51 = 12.09 ≈ 12.1 eV.

Question 11

According to Bohr's model, what is the radius of the first Bohr orbit (n=1) in a hydrogen atom? (Use a₀ = 0.53 Å)

Accepted Answer

The first Bohr radius (a₀) is by definition 0.53 Å, also known as the Bohr radius.

Question 12

An electron jumps from n=4 to n=2 in a hydrogen atom. Find the wavelength of the emitted photon. (Use hc = 1240 eV·nm, E₄ = -0.85 eV, E₂ = -3.4 eV)

Accepted Answer

ΔE = E₂ - E₄ = -3.4 - (-0.85) = -2.55 eV; wavelength λ = hc/|ΔE| = 1240/2.55 ≈ 486 nm.

Question 13

What is the maximum number of electrons that can occupy the M shell (n=3) of an atom?

Accepted Answer

Maximum electrons in shell n is 2n²; for n=3: 2(3)² = 2(9) = 18 electrons.

Question 14

In the Bohr model of hydrogen, what is the orbital angular momentum of an electron in the second Bohr orbit (n=2)?

Accepted Answer

Bohr's quantization rule states L = nℏ; for n=2, L = 2ℏ.

Question 15

According to Bohr's model, the radius of the first Bohr orbit (n=1) of a hydrogen atom is approximately 0.53 Å. What will be the radius of the third Bohr orbit (n=3)?

Accepted Answer

Bohr radius is proportional to n²; r_n = r₁ × n², so r₃ = 0.53 × 9 = 4.77 Å.

Question 16

The energy of an electron in the second orbit of a hydrogen atom is -3.4 eV. What is the energy of the electron in the first orbit?

Accepted Answer

Energy in Bohr model is inversely proportional to n²; E_n = E₁/n², so E₁ = E₂ × 4 = -3.4 × 4 = -13.6 eV.

Question 17

An electron transitions from n=4 to n=2 in a hydrogen atom. What is the wavelength of the emitted photon? (Use Rydberg constant R = 1.097 × 10⁷ m⁻¹)

Accepted Answer

Using 1/λ = R(1/n₁² - 1/n₂²) = 1.097 × 10⁷(1/4 - 1/16) = 2.056 × 10⁶ m⁻¹; λ ≈ 486 nm.

Question 18

Which of the following correctly defines the principal quantum number (n) in the context of atomic structure?

Accepted Answer

The principal quantum number n directly determines the energy level and the average orbital radius of electrons in an atom.

Agniveer Army Technical Atoms

Atoms — Practice Questions