calculate the wavelength of the Lyman line of the hydrogen spectrum in which yhe innitial quantum number,n is 5.?

Rydberg constant, R = 1.097 × 10⁷ /m
Corresponding to Lyman series, an electron fall from a higher energy level to n = 1.

Rydberg equation: 1/λ = R [(1/n₁²) - (1/n₂²)]
1/λ = (1.097 × 10⁷ /m) × [(1/1²) - (1/5²)] = (1.097 × 10⁷) × 24 / 25 /m
Wavelength λ = 25 / [(1.097 × 10⁷) × 24] m = 9.496 × 10⁻⁸ m = 94.96 nm

Lyman series .....

Spectral lines in the Lyman series represent transitions from higher energy levels to n=1. Following is the derivation of the equation to solve for wavelength in meters. We start with basic definitions.
E = -R(1/n²) .......... where R = 2.18x10^-18J ... Rydberg constant in Joules
ΔE = -R(1/n²(final) - 1/n²(initial))
ΔE = -hv = -hc/λ
-hc/λ = -R(1/n²(final) - 1/n²(initial))
λ = (hc/R) / (1/n²(final) - 1/n²(initial))
λ = (6.63x10^-34 Js x 3.00x10^8 m/s / 2.18x10^-18J) / (1/1 - 1/25)
λ = 9.50x10^-8 m .... or .... 95.0 nm

1/lambda = R(1 - (1/n^2))
where R = 1.0968 x 10^7 m^(-1).

When n = 5, the lambda comes out to 95.0 nm.