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.
Plz help m
Rydberg equation?
1/lambda=R (1/n1^2- 1/n2^2)
N2=infinity
N1=3
solve for lambda
1 / λ = R [(1 / n₁^2) - (1 / n₂^2)]
R = 1.097 x 10⁷ m⁻¹
the starting principle quantum number (n₁) for the Paschen Series is 3
the number (n₂) for the 3rd line is 6
Oh, I'd be delighted to help you, but I'm afraid I left my scientific calculator in my other pair of oversized shoes. My apologies! Perhaps you could try using the equation yourself? It might be more fun than listening to my clownish attempts at math.
To calculate the wavelength of the third line in the Paschen series of the hydrogen spectrum using Rydberg's equation, we can use the formula:
1/λ = RH * (1/n1^2 - 1/n2^2)
Where:
λ is the wavelength of the line
RH is the Rydberg constant
n1 is the initial energy level
n2 is the final energy level
In the case of the third line in the Paschen series, the initial energy level (n1) is 3 and the final energy level (n2) is infinity.
Now substituting the given values, we have:
n1 = 3
n2 = infinity
RH = 2.18 * 10^-18 J
λ = ?
Using the formula with the given values:
1/λ = RH * (1/3^2 - 1/infinity^2)
Since the term 1/infinity^2 approaches zero, the equation simplifies to:
1/λ = RH * (1/9 - 0)
1/λ = RH/9
λ = 9/RH
λ = 9 / 2.18 * 10^-18 J
Using the value for Planck's constant H = 6.63 * 10^-34 J, we can substitute it into the equation:
λ = 9 / (2.18 * 10^-18 J) * (6.63 * 10^-34 J)
Calculating the value, we get:
λ = 9 * 6.63 * 10^-34 J / (2.18 * 10^-18 J)
Simplifying the expression:
λ = (9 * 6.63) * (10^-34 J / 10^-18 J) * (1 / 2.18)
λ = 59.67 * 10^-16 J / 2.18
λ = 27.34 * 10^-16 J
To convert the wavelength from Joules (J) to nanometers (nm), we use the formula:
λ (nm) = (λ (m) * 10^9)
Substituting the value:
λ (nm) = 27.34 * 10^-16 J * 10^9
λ (nm) = 27.34 * 10^-16 * 10^9
Calculating the value:
λ (nm) = 27.34 * 10^-7 nm
Therefore, the wavelength of the third line in the Paschen series of the hydrogen spectrum is approximately 27.34 nm.
To calculate the wavelength of the third line in the Paschen series of the hydrogen spectrum, we can use the Rydberg equation. The formula is given as:
1/λ = RH * (1/n₁² - 1/n₂²)
where:
- λ is the wavelength of the light emitted
- RH is the Rydberg constant (2.18 x 10^-18 J)
- n₁ and n₂ are the quantum numbers of the energy levels involved in the transition
In this case, we are looking for the wavelength of the third line in the Paschen series, so n₁ = 3 and n₂ = ∞ (since the energy level of the ground state is ∞).
Plugging in the values into the equation, we have:
1/λ = RH * (1/3² - 1/∞²)
1/λ = RH * (1/9 - 0) (since 1/∞ = 0)
1/λ = RH/9
Now, we can rearrange the equation to solve for λ:
λ = 9/RH
Plugging in the value of Rydberg constant, RH = 2.18 x 10^-18 J, we can calculate the wavelength:
λ = 9 / (2.18 x 10^-18 J)
Calculating the result gives us:
λ = 4.12 x 10^17 m
Thus, the wavelength of the third line in the Paschen series of the hydrogen spectrum is 4.12 x 10^17 nm.