9/25 Friday Problem Solving Set #3

+ Extension Question from 9/11 Friday Problem Solving Set #2 + 9/22 ACER Pilot Session #3

List the following in order of energy from lowest to highest:

Blue, Green, Infrared, Orange, Purple/violet, Red, Ultraviolet, X-ray, Yellow

Infrared, Red, Orange, Yellow, Green, Blue, Purple/Violet, Ultraviolet, X-ray

Draw four 3d orbitals

Order the electron subshells from 1s to 5d, in order of lowest to highest energy.

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 4f 5d

Describe Rydberg’s Equation (as well as the two constants) and the order of the initial and final principal quantum numbers.

Rydberg’s constant R for wavelength: 1.097 × 10⁷ m^-1

Rydberg’s constant R for frequency: 3.29 × 10¹⁵ Hz

You may have to flip the final and initial principal quantum numbers to ensure that the result is a positive number. The smaller quantum number should come first, so that the first fraction is larger.

What is the Rydberg’s constant for energy formula (for hydrogen atoms)? How is it derived?

2.18 × 10^-19 J

It can be derived from Planck’s equation E = hv = hc/λ and the Rydberg constant by either:

• Multiply Rydberg constant for frequency by h (E = hv): 3.29 × 10¹⁵ Hz × 6.646 × 10^-34 Js

• Multiply h and c and divide by Rydberg constant for wavelength (E = hc/λ): 6.646 × 10^-34 Js × 3 × 10⁸ m/s / (1.097 × 10⁷ m^-1)

How do you find the concentration of an unknown by using a calibration curve?

Plug the absorbance of the unknown into the y-value for the calibration curve’s slope equation. Don’t forget that the slope is molar absorptivity/molar extinction coefficient ε.

This is a systematic error. Different wavelengths were used to measure the unknown and to create the calibration curve.

• The unknown was measured at 250 nm which resulted in log(ε) = 4.2, or ε = 10^4.2.

• The solutions making up the calibration curve were measured at 270 nm which resulted in log(ε) = 3.7, or ε = 10^3.7.

This means that the absorbance of the unknown is higher than it would have been if it had been measured at the same wavelength as the calibration curve.

It can be corrected by multiplying the calculated unknown concentration by the ratio between ε₂₇₀ and ε₂₅₀ (in this case 10^3.7/10^4.2). This is possible because Beer Lambert’s law A=εlc claims that absorbance and molar absorptivity is proportional. If ε is lower than A will also be lower.