The first excited state of the hydrogen atom is separated from the ground state by 10.2 eV.

(a) At what wavelength does this occur and what is the energy difference in kJ mol-1 between the ground and excited states? Show your working in each case.
(b) If the degeneracy of the ground state and the excited state is 1, calculate N* / N0 at 2,000 K and 8,000 K.

I barely understand this

a)Convert 10.2 ev to joules.

E = hc/wavelength.
You know E (joules) and h and c, calculate wavelength in meters. The 10.2 ev is the energy difference per photon, you want a mole of photons for kJ/mol.

b) I don't understand.
BTW, we like for you to use the same screen name for your posts. It helps us keep people straight.

If a 30.0L tank of laughing gas contains 2.74 moles of N2O at 25 degrees C what is the pressure (atm) in the tank?

No worries! I will explain step by step how to solve each part of the question.

(a) To find the wavelength at which the transition from the ground state to the first excited state occurs, we can use the formula:

E = hc/λ

where E is the energy difference between the states (10.2 eV), h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength we want to find.

First, let's convert the energy difference from eV to joules:
10.2 eV = 10.2 * 1.6 x 10^-19 J = 1.632 x 10^-18 J

Now we can rearrange the formula to solve for λ:
λ = hc/E

λ = (6.626 x 10^-34 J·s * 2.998 x 10^8 m/s) / (1.632 x 10^-18 J)

Calculating this gives us:
λ = 1.212 x 10^-7 m

So the wavelength is approximately 1.212 x 10^-7 meters.

To find the energy difference in kJ/mol, we will use Avogadro's constant (N₀ = 6.022 x 10^23 mol^-1).

Energy difference in kJ/mol = (1.632 x 10^-18 J * N₀) / (1000 J/kJ)

Calculating this gives us:
Energy difference = 270.7 kJ/mol (approximately)

(b) To calculate N* / N₀ at a given temperature, we need to use the Boltzmann distribution formula:

N* / N₀ = exp(-ΔE/RT)

where ΔE is the energy difference between the states (10.2 eV, which we previously converted to joules), R is the gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin.

For 2,000 K:
N* / N₀ = exp(-(1.632 x 10^-18 J)/(8.314 J/(mol·K) * 2000 K)

Calculating this gives us:
N* / N₀ = 2.201 x 10^-48 (approximately)

For 8,000 K:
N* / N₀ = exp(-(1.632 x 10^-18 J)/(8.314 J/(mol·K) * 8000 K)

Calculating this gives us:
N* / N₀ = 4.251 x 10^-193 (approximately)

So, at 2,000 K, N* / N₀ is approximately 2.201 x 10^-48, and at 8,000 K, N* / N₀ is approximately 4.251 x 10^-193.