Question

The wavelength of the four Balmer series lines for hydrogen are found to be 410.1, 434.3, 486.6, and 655.9 nm. What average percentage difference is found between these wavelength numbers and those predicted by 1 λ = R 1 nf2 − 1 ni2 ? It is amazing how well a simple formula (disconnected originally from theory) could duplicate this phenomenon.

Answer 1

Okay, If we use the theoretical formula as

1/ = R (1 / n_f² - 1 / n_i²)

where R is Rydberg's constant = 1.097e7 m⁻¹

n_f ( final level for Balmer series) = 2

so,

for n = 3 to n = 2

1/ = 1.097e7 (1 / 4 - 1/9)

= 656.33 nm

for n = 4 to n = 2

1/ = 1.097e7 (1 / 4 - 1/16)

= 486.17 nm

for n = 5 to n = 2

1/ = 1.097e7 (1 / 4 - 1/25)

= 434.1 nm

for n = 6 to n = 2

1/ = 1.097e7 (1 / 4 - 1/36)

= 410.2 nm

Therefore, the percentage difference is

% difference = (found value - calculated value / calculated value) * 100

for n = 3 to n = 2, % difference = 0.065 %

for n = 4 to n = 2 , % difference = 0.088 %

for n = 5 to n = 2, % difference = 0.046 %

for n = 6 to n = 2, % difference = 0.024 %