Wavenumber calculations

Question 1

Wavelengths in visible spectrum are in the range of 400 to 700nm.

1nm = 10^-9m

Use this info (and wave number formula) to show that a typical line in the Lyman series will be seen in the UV part of the spectrum, BUT only first four lines of the Balmer series will be seen in the visible region.

Answer 1

They want answers in wavelength.

Lyman series = m = 1, n = 2, 3, 4

Balmer series = m = 2, n = 3, 4, ,5, 6, 7

Lyman series

where m = 1, n = 2 aka 1st line

wave number = 82,275 cm^-1

Since wave number = 1 / λ

Therefore, 1 / 82275 cm

= 1.215 x 10^-5 cm

Now express in nm = wavelength

1.215 x 10-5 cm x 10⁷ = 121.5 nm (NOT b/w 400 to 700nm therefore in UV spectrum NOT visible region).

Balmer series

where m = 2, n = 6 aka 4th line

wave number = 1 / λ = R_H (1/m² - 1/n²)

λ = 1.097 x 10⁵ (1/2² - 1/6²)

= 109700 x (1/4 - 1/36)

= 109700 x (0.25 - 0.277…)

= 109700 x (0.22…)

wave number = 24,377.78 cm^-1

Calculator type in = 1.097x10⁵ (1/2² - 1/6²) = 24,377.78 cm^-1

wavelength in cm = 1/24,377.78 cm

= 4.102 x 10^-5 cm

wavelength in nm = 4.102 x 10^-5 x 10⁷ = 410.2 nm therefore in visible region.

where m = 2, n = 7 aka 5th line

25186.224 cm^-1

1 / 25186.224 = 3.97 x10^-5 cm

3.97 x10^-5 x 10⁷ = 397 nm therefore NOT in visible region.

Question 2

What are the two different formulas to calculate wave number?

Answer 2

wave number (cm^-1) = 1/λ

and

wave number (cm^-1) = R_H (1/m² - 1/n²)

where m = no. of series e.g. Lyman series, m = 1

where n>m

Question 3

What is the Rydberg constant, include units?

Answer 3

1.097 x 10⁵ cm^-1

Question 4

What is the formula to calculate wavelength (nm) λ?

Answer 4

λ = 1/wave number in cm.

convert cm to nm by multiplication.

cm to nm = x10⁷