Use Rydbuz equation to calculate the
wavelength of the third line in the paschen
series of the hydrogen spectrum.give ur
answer in Nm. RH=2.18 * 10^-18j, H=6.63 * 10^-34J.
To calculate the wavelength of the third line in the Paschen series of the hydrogen spectrum using the Rydberg equation, we need the formula as follows:
1/λ = R_H * (1/(n_1^2) - 1/(n_2^2))
Where:
λ is the wavelength of the spectral line
R_H is the Rydberg constant for hydrogen,
n_1 is the principal quantum number of the initial energy level,
and n_2 is the principal quantum number of the final energy level.
In this case, we are looking for the wavelength of the third line in the Paschen series, which corresponds to the transition from the n_1 = 5 energy level to the n_2 = 3 energy level.
Now, substituting the given values into the formula:
n_1 = 5
n_2 = 3
R_H = 2.18 x 10^-18 J
H = 6.63 x 10^-34 J
1/λ = R_H * (1/(n_1^2) - 1/(n_2^2))
1/λ = 2.18 x 10^-18 J * (1/(5^2) - 1/(3^2))
1/λ = 2.18 x 10^-18 J * (1/25 - 1/9)
1/λ = 2.18 x 10^-18 J * (9/225 - 25/225)
1/λ = 2.18 x 10^-18 J * (-16/225)
1/λ = -0.1552 x 10^-18 J
Finally, to find the wavelength (λ), we can take the reciprocal of -0.1552 x 10^-18 J:
λ = -1/(-0.1552 x 10^-18 J)
λ = 6.445 x 10^17 Nm
Therefore, the wavelength of the third line in the Paschen series of the hydrogen spectrum is approximately 6.445 x 10^17 Nm.