Certainly! Here's an AP Physics 2 Exam question related to atomic structure:

Question:

A hydrogen atom in its ground state undergoes a transition from the n = 2 energy level to the n = 1 energy level. Calculate the energy change (in joules) that occurs during this transition.

Given:

• Charge of an electron (e): 1.6 × 10^-19 C
• Planck's constant (h): 6.63 × 10^-34 J·s
• Speed of light (c): 3.00 × 10^8 m/s
• Permittivity of free space (ε₀): 8.85 × 10^-12 C²/N·m²
• Bohr radius (a₀): 5.29 × 10^-11 m

Answer & Explanation:

The energy change (ΔE) during the transition of an electron in a hydrogen atom can be calculated using the formula:

ΔE = E₂ - E₁ ΔE = -hcR(1/n²f - 1/n²i)

Where: ΔE = Energy change h = Planck's constant (6.63 × 10^-34 J·s) c = Speed of light (3.00 × 10^8 m/s) R = Rydberg constant (2.178 × 10^-18 J) n = Principal quantum number

Given: n₁ = 2 (initial energy level) n₂ = 1 (final energy level)

Using these values, we can calculate the energy change:

ΔE = -hcR(1/1² - 1/2²) ΔE = -hcR(1 - 1/4) ΔE = -hcR(3/4)

Now substitute the given values of h, c, and R into the equation: ΔE = -(6.63 × 10^-34 J·s)(3.00 × 10^8 m/s)(2.178 × 10^-18 J)(3/4) ΔE = -4.736 × 10^-23 J

Therefore, the energy change that occurs during the transition from the n = 2 to the n = 1 energy level in a hydrogen atom is -4.736 × 10^-23 J.

This calculation demonstrates the use of quantum mechanics and the Bohr model to determine the energy changes associated with electron transitions in the atomic structure.