Question

Calculate the dimensional formula for rydberg's constant.

Answer 1

Rydberg formula expressed wave number in terms of constant common to all series of lines known as Rydberg constant.

Rydberg formula defines the relationship of frequencies in one series of lines.Rydberg formula: N = R [1/(n+a)2 – 1/ (m + b)2] where N is wave number, R is Rydberg constant; m and n are integers, m is greater than n; and a and b are constants for particular series.

Mathematically,
Rydberg constant (R) = me4 / 8π ε02 h2
wherem = electron mass
e = electron charge
ε0 = permittivity of free space
h = Planck’s Constant

so putting all the dimensional formulas in the above equation we get

Dimensional formula of Rydberg constant = [M1L0T0] [M0L0A1T1]4 / [(M-1L-3T4A2)2] [(M1L2T-1)2] ]

Dimensional formula of Rydberg constant = M0L-1T0
SI unit of Rydberg constant is m-1

Answer 2

⇒ 1/λ = R[1/n₁² - 1/n₂²]

Since , n₁ & n₂ are constants neglecting them

⇒ 1/λ = R

⇒ R = 1/λ

⇒ Since λ has a unit m which is a length ,

⇒ [R] = [L]^-1

also , it can be written as [M^0 L^-1 T^0]