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.
Step plz
To calculate the wavelength of the third line in the Paschen series of the hydrogen spectrum using the Rydberg formula, you'll need to follow these steps:
Step 1: Understand the Rydberg formula.
The Rydberg formula is used to calculate the wavelength of the spectral lines in the hydrogen spectrum. It is given by:
1/λ = RH * (1/n1^2 - 1/n2^2)
Where:
λ is the wavelength of the spectral line.
RH is the Rydberg constant (2.18 * 10^-18 J).
n1 and n2 are integers representing the energy levels of the electrons involved in the transition.
Step 2: Identify the energy levels involved.
In the Paschen series, the transition occurs from energy level n1 to energy level n2, where n1 = 4 and n2 = 3. The third line in the Paschen series corresponds to n1 = 4 and n2 = 3.
Step 3: Substitute the values into the Rydberg formula.
Substituting the given values into the formula, we get:
1/λ = RH * (1/4^2 - 1/3^2)
Step 4: Simplify the equation.
Evaluate the fractions:
1/λ = RH * (1/16 - 1/9)
1/λ = RH * (9 - 16)/144
1/λ = RH * (-7)/144
Step 5: Calculate the wavelength.
To find the wavelength, take the reciprocal of both sides of the equation:
λ = 144 / (RH * (-7))
λ = -144 / (RH * 7)
Step 6: Substitute the given value of RH.
Substituting the given value for RH, which is 2.18 * 10^-18 J, we get:
λ = -144 / (2.18 * 10^-18 * 7)
Step 7: Simplify the equation and calculate the wavelength.
Evaluate the expression:
λ = -144 / (15.26 * 10^-18)
λ ≈ -9.42 * 10^-18 m
Since wavelength cannot be negative, take the absolute value:
λ ≈ 9.42 * 10^-18 m
Converting to nanometers (nm):
λ ≈ 9.42 * 10^-9 nm
So, the wavelength of the third line in the Paschen series of the hydrogen spectrum is approximately 9.42 * 10^-9 nm.