Promotion of an electron from the ground state (n=1) to n=2
Electron jumps in the hydrogen spectrum
Lyman series (ultra-violet radiation) corresponds to transitions between higher shells and the ground state (n=1)
ΔE = h ν
c = ν λ
c = ν λ
as
ν = c ÷ λ
The convergence limit for the sodium atom has a frequency of 1.24 × 1015 s−1. Calculate the first ionisation energy of sodium in kJ mol−1.
Answer:
Step 1: Write out the equation to calculate the first ionisation energy (IE1)
ΔE = h ν
Step 2: Substitute in numbers from question and data booklet to give energy change per atom
IE1 = 6.63 × 10−34 × 1.24 × 1015
IE1 = 8.22 × 10−19 J atom−1
Step 3: Calculate the first ionisation energy per mole by multiplying by Avogadro's constant
IE1 = 8.22 × 10−19 × 6.02 × 1023
IE1 = 494 916 J mol−1
Step 4: Convert J mol−1 to kJ mol−1 by dividing by 1000
IE1 = 495 kJ mol−1
So the first ionisation energy (IE1) of sodium has been calculated as 495 kJ mol−1
The convergence limit for the hydrogen atom has a wavelength of 91.16 nm. Calculate the ionisation energy for hydrogen in kJ mol−1.
Answer:
Step 1: Calculate the frequency of the convergence limit, converting wavelength into m (nm to m = × 10−9)
c = ν λ
ν = c ÷ λ
ν = 3.00 × 108 ÷ 91.16 × 10−9
ν = 3.29 × 1015 s−1
Step 2: Substitute into the equation to calculate IE1 for one atom of hydrogen in J mol−1
ΔE = h ν
IE1 = 6.63 × 10−34 × 3.29 × 1015
IE1 = 2.18 × 10-18 J atom−1
Step 3: Calculate IE1 for 1 mole of hydrogen atoms
IE1 = 2.18 × 10−18 × 6.02 × 1023
IE1 = 1 313 491 J mol−1
Step 4: Convert J mol−1 to kJ mol−1
IE1 = 1313 kJ mol−1
So the first ionisation energy (IE1) of hydrogen has been calculated as 1313 kJ mol−1
These equations are found in the data booklet so you don't need to learn them.Also, be careful to calculate the first ionisation energy (IE1) per mole by using Avogadro's constant (NA) 6.02 × 1023 and converting units to kJ mol−1.Finally, when working through calculations, keep the numbers in your calculator to avoid rounding up too early.
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