In an experiment you measure a first-order red line for Hydrogen at an angle difference of ΔΘ = 22.78o. The diffraction grating you are using has 5900 lines per cm.
a) What is the wavelength of this light?
b) What is the value of Rydberg’s constant for this measurement?
Answer:
a) wavelength = 656.3 nm
b) the value of Rydberg’s constant for this measurement is 1.097 × 10⁷ m⁻¹
Explanation:
Given that;
angle of diffraction Θₓ = 22.78°
incident angle Θ₁ = 0
slit separation d = 5900 lines per cm = 1/5900 cm = 10⁻²/5900 m = 0.01/5900 m
order of diffraction n = 1
wavelength λ = ?
to find the wavelength, we use the expression
λ = d (sinΘ₁ + sinΘₓ) / n
To find the wavelength λ;
λ = 0.01/5900 × (sin0 + sin22.78° )
λ = 6.5626 × 10⁻⁷ m
λ = 656.3 x 10⁻⁹ m
∴ λ = 656.3 nm
b)
According Balnur’s series spectral lines; n₁ = 3, n₂ = 2 and
λ = R [ 1/n₂² – 1/n₁²]
where R is Rydberg’s constant
from λ = R [ 1/n₂² – 1/n₁²]
R = 1/λ [n₂²n₁² / n₁² – n₂²]
R = 10⁹/ 656.3 [ 9 × 4 / 9 – 4 ]
R = 1.097 × 10⁷ m⁻¹
Therefore the value of Rydberg’s constant for this measurement is 1.097 × 10⁷ m⁻¹