Earth 1 Knowledge Test

Question 1

What is the energy of hydrogen's ground state (n = 1)?

Accepted Answer

−13.6 eV

Question 2

Using Eₙ = −13.6 eV/n², what is E₂?

Accepted Answer

−3.4 eV

Question 3

Why must the magnetic quantum number m be a whole number?

Accepted Answer

G(φ) = e^{imφ} must return to itself after one full turn, φ → φ + 2π

Question 4

For n = 3, which values can ℓ take?

Accepted Answer

0, 1, 2

Question 5

For ℓ = 2, how many values of m are allowed?

Accepted Answer

5

Question 6

How many radial nodes does the 3s orbital have?

Accepted Answer

2

Question 7

How many states (ignoring spin) share the n = 3 energy?

Accepted Answer

9

Question 8

In the separation of variables, the constant C turns out to equal…

Accepted Answer

ℓ(ℓ + 1)

Question 9

Why is ψ·e^{−iEt/ħ} called a stationary state?

Accepted Answer

|e^{−iEt/ħ}| = 1, so |ψ|² never changes in time

Question 10

Roughly how big is the Bohr radius a₀?

Accepted Answer

0.053 nanometres (0.53 Å)